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1)

(a) We just quoted Rebbi Avahu Amar Rebbi Yochanan, in whose opinion Heter only combines with Isur to make up the Shiur for Malkos regarding the Isurim of Nazir. Based on the Pasuk "Ki Chol Se'or ve'Chol D'vash Lo Saktiru Mimenu Isheh la'Hashem" - Ze'iri holds that it also applies to the La'av of Se'or (burning yeast on the Mizbei'ach).

(b) Ze'iri holds like Rebbi Eliezer (who Darshens "Kol", wherever it appears in the Torah).

(c) He also holds 'Heter Mitztaref le'Isur' - with regard to Chametz on Pesach.

(a) The reason that Ze'iri added the La'av of burning Se'or on the Mizbei'ach (with regard to 'Heter Mitztaref le'Isur'), and not that of Chametz on Pesach, is to counter Abaye - who says that one is Chayav for burning even less than a k'Zayis of yeast on the Mizbei'ach.

(b) Abaye learns this from "Kol". From "*Ki* Chol he learns - that one is even Chayav on a mixture of Matzah that contains yeast (We are learning all the D'rashos according to the opinion of Tosfos).

(c) According to Rava (like whom Ze'iri holds), a Kohen who offers less than a k'Zayis is Patur even according to Rebbi Eliezer. He learns from ...

1. ... "Kol" - that one is also Chayav for burning less than the entire fistful of yeast (i.e. two k'Zeisim, provided it is at least a k'Zayis).
2. ... "Ki Chol" - that one is even Chayav in a case of 'Heter Mitztaref le'Isur'.

(d) Abaye Darshens the word "Kol" in connection with Chametz to include 'Heter Mitztaref le'Isur' and not to include less than a k'Zayis (like he does by the La'av of 'Se'or') is - because the Torah uses the term 'Achilah' by Chametz (and 'Achilah' always implies at least a k'Zayis).

(a) If a T'vul-Yom (who is a Sheini, and can therefore only affect T'rumah, but not Chulin) touches any part of a T'rumah-stew containing Chulin spices, he renders the entire stew, Tamei (because the stew is the Ikar, and the spices secondary). In the reverse case, if he touches the spices in a Chulin-stew containing T'rumah spices - he only renders the location which he touched, Pasul (i.e. a Sh'lishi, which cannot transmit Tum'ah further by T'rumah).

(b) According to Rashi, we then ask why even that is Pasul, seeing as the spices are Batel to the stew. Tosfos (Rabeinu Tam) rejects this text for a number of reasons. According to them - the Kashya is why the spices should become Tamei, seeing as they comprises less than a k'Beitzah, which is not subject to Tum'ah.

(c) Rashi rejects Tosfos version - because, in his opinion, although less than a k'Beitzah of food cannot transmit Tum'ah, it is itself subject to Tum'ah.

(d) Rav Dimi does not answer that 'Pasal' means mi'de'Rabbanann (which it would in any case be) - because the Lashon 'Pasal' (unqualified) implies mi'd'Oraysa.

(a) Rabah bar bar Chanah Amar Rebbi Yochanan ascribes the fact that he is Chayav for subsequently eating it (and that the Terumah is not Batel), to the fact that a Zar receives Malkos for eating a k'Zayis. Abaye, who explains this to mean that he receives Malkos for eating an overall k'Zayis (incorporating Heter and Isur), a proof that 'Heter Mitztaref le'Isur' applies even to other Isurim too (and is not confined to a Nazir [a Kashya on Rebbi Avahu Amar Rebbi Yochanan and Ze'iri).

(b) 'Lokeh' really means - that he would receive Malkos if the basic Terumah were d'Oraysa (which is fact, it is not, because the Terumah of garlic is only mi'de'Rabbanan).

(c) Rav Dimi refutes Abaye's proof by interpreting Rabah bar bar Chanah Amar Rebbi Yochanan to mean - that he would be Chayav Malkos for eating a k'Zayis (not because of 'Heter Mitztaref le'Isur', but) because there was a 'k'Zayis bi'Chedei Achilas P'ras' (for which he is Chayav according to the Rabbanan no less than according to Rebbi Eliezer). A 'k'Zayis bi'Chedei Achilas P'ras' - is a ratio of at least one k'Zayis of Isur per four k'Beitzim of mixture. (The time it takes to eat four egg-volumes is also the maximum time period within which one must eat a k'Zayis of any Isur in order to be Chayav).

(d) The source for the Shiur of 'k'Zayis bi'Chedei Achilas P'ras' - is 'Halachah le'Moshe mi'Sinai'.

(a) We just attributed the spices not becoming Batel in the stew to the fact that one would receive Malkos for eating a 'k'Zayis bi'Chedei Achilas P'ras' of the stew with the spices. The problem with this, according to Rabeinu Tam, who explained the Kashya in connection with the fact that there was less than a k'Beitzah of Tum'ah is - that, since we are not talking about eating, only rendering the spices Tamei, this has nothing to do with 'K'dei Achilas P'ras', but with 'Heter Mutztaref le'Isur', for which according to Rav Dimi, one does not receive Malkos (even if one were to eat them together).

(b) Rabeinu Tam will answer - that although 'Heter Mitztaref le'Isur will not be effective to make up the Shiur (according to Rav Dimi), it will however, be effective to obligate him, if he were to eat an entire Shiur of a k'Zayis together with a P'ras (four k'Beitzim) of Heter. This is because, without the Heter, he would not be Chayav for eating spices only (which one does not tend to eat that way) on their own.

6)

(a) Abaye asks whether a k'Zayis bi'Chedei Achilas P'ras is d'Oraysa. We already know from the Mishnah in Kerisus that 'Kol ha'Ochlin Mitztarfin bi'Chedei Achilas P'ras' - but only when the two species concerned are separate, and not when they are mixed such as in our case (Tosfos).

(b) Abaye knows that he is not Chayav because of 'Ta'am k'Ikar' (which he himself will shortly learn from "Mishras" - because he currently holds that 'Ta'am k'Ikar' only applies where one eats the entire k'Zayis in one gulp (e.g. if he swallowed a k'Zayis of wine absorbed by two k'Zeisim of bread), but not if he ate it bit by bit.

(c) Rav Dimi replies that the Chiyuv Malkos of which Rebbi Yochanan speaks is when he eats a 'k'Zayis bi'Chedei Achilas P'ras'. Nevertheless, the Rabbanan argue with Rebbi Eliezer and exempt someone who eats Kutach ha'Bavli (despite the fact that it contains a 'k'Zayis bi'Chedei Achilas P'ras') from Malkos - because Kutach ha'Bavli is a sharp condiment, which one tends to eat in small quantities (in which case one would not normally eat a k'Zayis within a K'dei Achilas P'ras).

(d) The author of the Mishnah of 'Mikpeh' (which declares the spices in a T'rumah-stew touched by a T'vul-Yom Pasul) however - could also be the Rabbanan, who will agree with Rebbi Eliezer for the reason stated by Rebbi Yochanan ('Ho'il ve'Zar Lokeh Alehah bi'k'Zayis') Tosfos.

(a) Even if someone does eat a dishful of Kutach ha'Bavli within the required time limit - will not be Chayav (because this is not the normal way of eating it, and the principle of 'Batlah Da'ato Eitzel B'nei Adam' will apply).

(b) Abaye establishes the Machlokes between Rebbi Eliezer and the Rabbanan by 'Heter Mitztaref le'Isur', irrespective of how much one eats). He knows that the Rabbanan even argue in a case where one ate more than one 'k'Zayis bi'Chedei Achilas P'ras' (and not specifically where he ate only one k'Zayis of the stew) - because of their statement in Pesachim 'Al Chametz Dagan Gamur Anush Ka'res, al Eiruvo, *be've'Lo K'lum*', implying that one is Patur, irrespective of how much however much he ate.

(a) If two mortars full of spice, one of Chulin, the other of T'rumah, spilt into two pots, one of Chulin and the other, of T'rumah, we assume that the T'rumah fell into the T'rumah, and the Chulin into the Chulin - because by Isurim d'Rabbanan, we apply the principle of 'Tolin' (meaning that we place each one on its Chazakah, assuming that it remained as it was).

(b) Irrespective of the fact that a 'k'Zayis bi'Chedei Achilas P'ras' is d'Oraysa (as we just established), the Beraisa is lenient by T'rumah, to rely on 'Tolin' - because it is speaking about spices, whose basic status of T'rumah is only mi'd'Rabbanan.

(c) Before replying to Abaye's Kashya, we first point out that the same Kashya would apply if 'Heter Mitztaref le'Isur' were d'Oraysa (as he maintains). Abaye could not reply that the author of the Beraisa is the Rabbanan (who do not Darshen "Kol") - because he assumes that, if the author of the Beraisa of 'Mikpeh' is (also) Rebbi Eliezer, so is this one.

(a) Abaye then questions Rav Dimi from a Beraisa, where two Sa'ah of grain, one of Chulin and one of T'rumah, fell into two boxes, one of Chulin and one of T'rumah. Here too (like in the previous Beraisa), the Tana rules 'Tolin. Abaye is happy with this Beraisa - because he only holds 'Heter Mitztaref le'Isur' when the majority is Heter (but not when the Heter and the Isur are in equal proportions, as they are here).

(b) Nevertheless, in the two previous cases ('Kutach ha'Bavli' and the two mortars, neither of which contain a majority of Isur), the S'vara of 'Heter Mitztaref le'Isur' applies - because, unlike the case of the two boxes (where the Isur is immediately Batel in the majority), the S'vara of 'Nosen Ta'am' applies (since in both cases, the Heter and the Isur are mixed, thereby preventing Bitul from taking place) Tosfos.

(c) In the case of the two boxes, where there is a majority of Heter, the Tana still requires 'Tolin', and is not satisfied with the fact that there is a majority of Heter to permit it - because by an Isur d'Oraysa, he requires two S'varos in order to permit the Isur (Tosfos).

(a) In spite of the way we just explained Abaye, the Tana nevertheless requires the S'vara of 'Tolin' in the case of the two boxes (rather than rely on that of Bitul alone) - because, if 'K'dei Achilas P'ras' were d'Oraysa, Chazal would have been stringent and forbidden the boxes on the basis of 'Bitul' alone (a decree because of 'Min be'she'Eino Mino').

(b) Abaye is nevertheless happy with the Beraisa. He in any case, will not apply the same S'vara (to apply 'Heter Mitztaref le'Isur' even to a case where there is more Heter than Isur, on account of when there is not) - because 'Heter Mitztaref le'Isur' never ever applies to a case where there is more Heter than Isur (unlike 'K'dei Achilas P'ras', which can sometimes apply to 'Min be'Mino' (seeing as he is eating Isur, which would be forbidden if it was recognizable).

(c) To refute Abaye's Kashya as to how the Tana can rely on 'Tolin' in face of an Isur d'Oraysa - because it is speaking about T'rumah bi'Zeman ha'Zeh, which is only d'Rabbanan.