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1)

(a) Abaye equates the Din of Nidah with that of a Sotah - inasmuch as a child born from either of them is not a Mamzer, and that, in the event that someone betroths either of them, his Kidushin is effective.

(b) When Abaye says 'ha'Kol Modim be'Ba al ha'Nidah ve'Al ha'Sotah ... ', when he says ...

1. ... 'Nidah' - he is referring to Shimon ha'Teimani, who holds 'Yesh Mamzer me'Chayvei K'riysus'.
2. ... 'Sotah' - he is referring to Rebbi Akiva, who holds 'Yesh Mamzer me'Chayvei La'avin'.

(c) Chizkiyah learns from the Pasuk "u'S'hi Nidasah Alav" - that Kidushin with a Nidah is effective.

(d) And what do we learn from the Pasuk in Naso "Acharei Asher Hutama'ah" - that Kidushin with a Sotah is valid.

(a) Rav Acha bar Ya'akov learns all the other Arayos from Yevamah le'Shuk - from a 'Kal va'Chomer' (if Kidushin with a Chayvei La'av is not valid, how much more so with Chayvei K'risus and Miysos Beis-Din.

(b) The problem with the Pasuk "Ki Siheyenah le'Ish Shtei Nashim ha'Achas Ahuvah ve'ha'Achas Senu'ah" (in connection with the birthright) is - why would one even think that the inheritance of the birthright would depend on the love or the hatred of the firstborn's father towards his mother?

(c) Rav Papa therefore interprets the Pasuk - to refer to the legality of the marriage (in other words, 'Senu'ah' refers to the fact that the parents had transgressed a La'av, and she is hated [by Hashem] in her marriage).

(d) We now learn from here - that the Kidushin of Chayvei La'avin is valid.

(a) Rav Papa's explanation will not work according to Rebbi Akiva - since, in his opinion, the Kidushin of Chayvei La'avin is invalid.

(b) Therefore according to him, we initially establish the Pasuk "Ki Siheyenah le'Ish ... " ('Senu'ah be'Nisu'ehah') by Almanah le'Kohen Gadol, like Rebbi Sima'i, who extrapolates from "ve'Lo Yechalel Zar'o - that the children of Chayvei La'avin of Kehunah are Chalalim, but not Mamzerim (in which case, Kidushin is effective, too).

(c) This answer however, will not work according to Rebbi Yeshevav, who says in Rebbi Akiva ' ... Kol she'Ein Lo Bi'ah be'Yisrael ha'V'lad Mamzer'. According to him, assuming that he ...

1. ... merely comes to counter Rebbi Sima'i - we will establish the Pasuk by Chayvei Asei.
2. ... is speaking in absolute terms - we will establish it by a Be'ulah le'Kohen Gadol.

(d) A Be'ulah le'Kohen Gadol is different than a Mitzri and Edomi in this regard - because it is an Asei that is not common to all (and is therefore considered a weak Asei).

(a) A Be'ulah is not forbidden to a Kohen Gadol on the grounds that she is a Zonah (despite the fact that she is neither a Gerushah nor an Almanah) - because a Zonah is a woman who has relations with someone to whom she is forbidden (as we learned in a Mishnah in Yevamos) but not for every illicit relationship.

(b) We just learned that the Rabbanan establish the Pasuk by Chayvei La'avin. They decline to establish the Pasuk ...

1. ... by two Mitzriyos - because they are both Senu'os (and we are searching for a case when one of the women is an Ahuvah and the other, a Senu'ah.
2. ... by a Yisre'elis and a Mitzris - because the Pasuk implies that the two women share the same nationality.
3. ... by a Yisre'elis and a Be'ulah le'Kohen Gadol - because the Pasuk makes no mention of a Kohen here.

(c) Rebbi Akiva nevertheless establishes the Pasuk in this way - because (in spite of the Rabbanan's argument) he says that we have to allow the Pasuk to establish itself (since we already know from a Yevamah that the Kidushin of Chayvei La'avin is ineffective). Consequently, if the only way to explain the Pasuk is by establishing it by a Kohen, so be it.

5)

(a) We learn from the Pasuk ...

1. ... (concerning Eliezer prior to the Akeidah) "Shevu Lachem Poh Im ha'Chamor" - that Kidushin with an Eved is invalid.
2. ... (concerning an Eved Ivri and a Shifchah Cana'anis) "ha'Ishah vi'Yeladehah Tih'yeh la'Adonehah" - that the children of a Shifchah Cana'anis are Avadim.

(b) And we learn from the Pasuk in Va'eschanan ...

1. ... "ve'Lo Sischaten Bam" (written in connection with the seven nations of Cana'an) - that Kidushin with a Nochri is invalid.
2. ... "Ki Yasir es Bincha me'Acharai" - that the children of a Nochris are Nochrim.

(a) Based on the previous Pasuk "ve'Lo Sischaten Bam, Bitcha Lo Siten li'Veno, u'Vito Lo Sikach li'Venecha", Rebbi Yochanan Amar Rebbi Shimon explains that the Pasuk "Ki Yasir es Bincha me'Acharai" ...

1. ... refers - to "Bitcha Lo Siten li'Veno", and it is about their son (who is a Yisrael) that the Torah is speaking.
2. ... not referring - to "u'Vito Lo Sikach li'Venecha", because their son is a Nochri.

(b) Ravina extrapolates from there - that the child of a Nochri and a bas Yisrael is considered a Yisrael (though it is unclear what Ravina is adding to what Rebbi Yochanan has already said [See Tosfos (DH 'Bincha')].

(c) We try and extrapolate from Ravina (from the fact that, in spite of the fact that the Kidushin of a Nochri and a Yisre'elis is invalid, their child is considered a Yisrael) - that, like other children who are born from unions where Kidushin are not valid (i.e. Chayvei K'riysus), the child should be a Mamzer.

(d) We refute this suggestion - by conceding that the child is not Kasher, but by falling short of calling him a Mamzer, only a Yisrael Pasul.

(a) The Pasuk "ve'Lo Sischaten Bam ... Ki Yasir ... ", from which we learned that Kidushin with a Nochri is not valid, is confined to the seven nations of Cana'an. We reject the proposal to extend this to other Nochrim because the Torah writes "Ki Yasir" (to include anyone who will lead your grandsons astray) - on the grounds that this D'rashah is only valid according to Rebbi Shimon, who Darshens the Torah's reasons even when they are not written, and according to whom "Ki Yasir" would therefore be superfluous.

(b) Rebbi Shimon says this in Bava Metzi'a - where he restricts the Mitzvah of returning a security to a poor widow, because he ascribes the reason for the Mitzvah is so as not to give her a bad name (since he will be obligated to come to her house each evening to return her article, and to retrieve it each morning, or vice-versa). Consequently, one may take a security from a rich widow, who does not require the article to be returned.

(c) According to the Rabbanan, we learn from the Pasuk ...

1. ... "Ki Yasir" - that it is only the seven nations that one is obligated to destroy, because their total dedication to idolatry poses a spiritual danger to K'lal Yisrael (unlike other nations, who only serve their idols by rote, because they are following their tradition, and who will not necessarily attempt to enforce their beliefs on Yisrael).
2. ... in Ki Seitzei (in connection with an Eishes Yefas To'ar) "ve'Achar-Kein Tavo Eilehah u'Ve'altah" - that the Kidushin of a Yisrael with a Nochris (even if she is not from the seven nations [or vice-versa]) is not valid.
3. ... there, "Ki Siheyenah le'Ish Sh'tei Nashim ... ve'Yaldu Lo" - that, wherever Kidushin is valid, the child is Misyaches to his father, but where is not (i.e. when the woman is from a different nation), then it is Misyaches to his mother.

(d) We ask why we cannot learn the equivalent Din by Shifchah from there too, and we answer - that indeed we do.

(a) Rebbi Yossi Hagelili in a Beraisa rules that if someone sets his Shifchah free but retains her unborn child, the child follows her to freedom. According to the Rabbanan - the master's condition stands.

(b) Immediately following the Rabbanan's opinion, the Tana continues 'Mishum she'Ne'emar "ha'Ishah vi'Yeladehah Tih'yeh la'Adonehah". Rava connects this Limud to the words of Rebbi Yossi Hagelili (in spite of their position in the Beraisa), according to whom they were obviously said.