(Something learned from) a Hekesh can teach through Kal va'Chomer;

We learn this from Tana d'Vei R. Yishmael (41a).

Question: Can a Hekesh teach through Binyan Av?

Answer (R. Yirmeyah) Question: Why did the Torah need to (make a Hekesh to) teach that Asham is slaughtered in Tzafon? We should be able to learn this from a Binyan Av from Chatas!

Answer: Since the Torah made such a Hekesh, this teaches that (what was learned from) a Hekesh (e.g. that Chatas is slaughtered in Tzafon) cannot teach through Binyan Av!

Rejection: If so, why can't we learn from a Binyan Av from Olah (in which it explicitly says that it must be slaughtered in Tzafon)?!

You must say, we cannot learn because there is a Pirchah. Olah is Kalil (totally consumed on the Mizbe'ach, but Asham is not);

Likewise, (even if we normally could learn a Binyan Av from a Hekesh), we cannot learn from Chatas, for it atones for Chayavei Kerisus!

Suggestion: Granted, we could not learn Asham from Olah or Chatas, even if Tzafon were explicit in both of these, due to Pirchos. However, perhaps the Torah could have written Tzafon regarding two of these, and we would learn the third from them!

Rejection: We could not learn any one from the others;

We could not learn Olah from Chatas and Asham, for they are Mechaper (more than Olah)!

We could not learn Chatas from Olah and Asham, for they are males!

We could not learn Asham from Olah and Chatas, for they are brought also for Korbanos Tzibur!

Question: Can (something learned from) a Gezerah Shavah teach through a Hekesh?

Answer (Rav Papa) "V'Zos Toras Zevach ha'Shelamim... Im Al Todah" teaches that Todah may be brought from money of Ma'aser Sheni, just like Shelamim;

We learned Shelamim from a Gezerah Shavah "Sham-Sham" from Ma'aser.

Objection (Mar Zutra brei d'Rav Mari): Ma'aser Sheni is Chulin! (All agree that we learn Lamed mi'Lamed in Chulin.)

Answer (Rav Papa): (I hold that) we consider the Lamed, and it is Kodesh.

Question: Can a Gezerah Shavah teach through a Gezerah Shavah?

Answer #1 (Rami bar Chama - Beraisa): "V'Soles Murbeches (is brought with a Todah)" teaches that Revuchah (Matzah loaves in which the flour is first scalded in boiling water) is made from Soles (choice flour);

We learn Chalos (regular Matzah loaves) from a Gezerah Shavah "Chalos-Chalos" to Revuchah;

We learn Rekikin (Matzah wafers) from a Gezerah Shavah "Matzos-Matzos" to Chalos.

Objection (Ravina): Perhaps the Gezerah Shavah "Matzos-Matzos" equates Rekikin to Chalos of Ma'afe Tanur (of Minchas Nedavah, regarding which it explicitly says Soles)!

Answer #2 (Rava - Beraisa): "V'Kirbo u'Firsho v'Hotzi" teaches that the Par Mashu'ach is taken intact outside Yerushalayim to be burned;

Suggestion: Perhaps it is burned intact!

Rejection: It says "Rosho" and "Kera'av" regarding Par Mashu'ach, like it says about Olah. Just like there it is dissected, also here.

Suggestion: Perhaps we flay the skin, just like we flay an Olah!

Rejection: It says "v'Kirbo u'Firsho."

Question: How do we learn this from "v'Kirbo u'Firsho"?

Answer (Rav Papa): (Earlier, the verse mentions the Or (skin) and Basar.) Just like the Peresh (excrement in the intestines) is left inside (it would be disgraceful to remove it), also the meat is left inside its skin.

(Beraisa - Rebbi): Regarding Par Yom Kipur, it mentions Or, Basar and Peresh, like it does regarding Par Mashu'ach. Just like Par Mashu'ach is dissected but not flayed, also Par Yom Kipur. (We learn from a Gezerah Shavah, and Par Mashu'ach itself was learned from a Gezerah Shavah to Olah.)

Question: Can a Gezerah Shavah teach through a Kal va'Chomer?

Answer #1: A Kal va'Chomer teaches that it can!

We cannot learn Hekesh mi'Hekesh (we learn this from Ravina or Rava), yet a Hekesh can teach through a Kal va'Chomer (we learn this from Tana d'Vei R. Yishmael);

A Gezerah Shavah can teach through a Hekesh (like Rav Papa taught), all the more so it can teach through a Kal va'Chomer!

Question: This is like Rav Papa, who says that we consider the Lamed. According to the opinion that considers the source, we have no source that a Gezerah Shavah can teach through a Hekesh (in Kodshim)!

Answer #2: We learn the Kal va'Chomer as follows:

A Hekesh cannot teach through Hekesh (Shitah Mekubetzes - nor Gezerah Shavah), but it can teach through a Kal va'Chomer;

A Gezerah Shavah can teach through another Gezerah Shavah (like Rami bar Chama taught). All the more so it can teach through a Kal va'Chomer!

Question: Can a Gezerah Shavah teach through a Binyan Av?

This question is not resolved.

Question: Can a Kal va'Chomer teach through a Hekesh?

Answer: A Kal va'Chomer teaches that it can!

A Hekesh cannot teach through Gezerah Shavah (like R. Yochanan taught), yet a Gezerah Shavah can teach through a Hekesh (according to Rav Papa);

A Hekesh can teach through Kal va'Chomer, all the more so Kal va'Chomer can teach through a Hekesh!

Question: This is like Rav Papa. According to the opinion that we consider the source, how can we answer?

This question is not resolved.

Question: Can a Kal va'Chomer teach through a Gezerah Shavah?

Answer: A Kal va'Chomer teaches that it can!

A Gezerah Shavah cannot be learned from (something learned from) a Hekesh, yet it can teach through a Gezerah Shavah;

A Kal va'Chomer can be learned from a Hekesh, all the more so it can teach through a Gezerah Shavah!

Question: Can a Kal va'Chomer teach through a Kal va'Chomer?

Answer #1: A Kal va'Chomer teaches that it can!

A Gezerah Shavah cannot be learned from a Hekesh, yet it can teach through a Kal va'Chomer (answers (b) and (d) above);

A Kal va'Chomer can be learned from a Hekesh, all the more so it can teach through a Kal va'Chomer!

This Kal va'Chomer is 'the son of' (i.e. derived from) a Kal va'Chomer.

Objection: This is the grandson of a Kal va'Chomer! (Rashi - one of the sources (1) was itself learned from a Kal va'Chomer ((b) or (d)). Perhaps we do not learn from something so far removed. Tosfos - we cannot use two Kal va'Chomers to show that we can derive laws from two Kal va'Chomers.)

Answer #2: A Kal va'Chomer (that does not rely on another Kal va'Chomer) teaches that it can!

We cannot learn Hekesh mi'Hekesh, yet Hekesh can teach through a Kal va'Chomer;

A Kal va'Chomer can be learned from a Hekesh, all the more so it can teach through a Kal va'Chomer!

This Kal va'Chomer is the son of a Kal va'Chomer.

Question: Can a Kal va'Chomer teach through a Binyan Av?

Answer (R. Yirmeyah - Beraisa - R. Meir): If a bird was found to be Treifah after Melikah was done, (it is not a Neveilah;) it does not have Tum'as Beis ha'Bli'ah (to be Metamei one who swallows a k'Zayis of it, and his garments);

R. Yehudah says, it has Tum'as Beis ha'Bli'ah (and even a slaughtered Treifah bird does).

R. Meir: A Kal va'Chomer teaches that it does not! Tum'as Neveilah of a Behemah is more severe than that of a bird. It is Metamei one who moves or touches it, yet Shechitah is Metaher a Treifah animal (i.e. it prevents it from becoming Neveilah). Nivlas Of is not Metamei one who moves or touches it, all the more so Shechitah is Metaher a Treifah bird;

Shechitah (of a healthy bird) permits eating it, and it is Metaher a Treifah bird. The same applies to Melikah!

R. Yosi says, Dayo (we cannot learn more than (either of) the sources of the Kal va'Chomer). Shechitah is Metaher it, like we find regarding Behemos, but Melikah is not.