Beis Hillel hold that this applies only to a Tam Bechor. A Ba'al Mum may be eaten "ka'Tzvi vecha'Ayal" (Chayos, which have no Kedushah);

A Tamei (Kohen) may not eat Kodshei Kalim, yet he may eat Bechor (Ba'al Mum). A (Tahor) Zar may eat Kodshei Kalim, all the more so he may eat Bechor!

Question: We cannot learn from a Tamei, for Tum'ah is permitted for Korbanos Tzibur (if they cannot be brought b'Taharah)!

Answer: We do not learn from offering b'Tum'ah, rather, from eating. (We never find something permitted to a Tamei Kohen and forbidden to a Zar.)

Question: R. Akiva permits even Nochrim. What is his reason?

Answer: "Ka'Tzvi vecha'Ayal" - just like deer and wild goats are permitted to Nochrim, also a Bechor Ba'al Mum.

Question: Why do Beis Hillel (in the Beraisa) argue?

Answer: Three verses mention Tzvi va'Ayal;

One of them teaches the laws of R. Yitzchak and R. Oshaya. (Tosfos - one who works with Pesulei ha'Mukdashim after it was redeemed or mates it (even with its own species) is lashed. The Torah considers it like two different species, "ka'Tzvi vecha'Ayal");

One of them teaches like R. Elazar Hakapar expounded (that Chayos must be slaughtered, just like animals);

The third teaches that just like Bechorah does not apply to Tzvi va'Ayal, it does not apply to Pesulei ha'Mukdashim.

(Beraisa - Beis Shamai) A Nidah may not eat Bechor (Ba'al Mum);

Beis Hillel permit.

Beis Shamai learn from "u'Vesaram Yihyeh Lach... " Just like a Nidah may not eat Chazeh v'Shok, she may not eat Bechor;

Beis Hillel say that applies only to a Tam Bechor. Regarding a Ba'al Mum it says "ha'Tamei veha'Tahor Yachdav"!

Beis Shamai say, that permits only a Tamei whose Tum'ah does not come from his own body. We find that the Torah distinguishes whether or not the Tum'ah come from his own body!

(Mishnah): When Korban Pesach is brought b'Tum'ah (because most of Yisrael or the Kohanim are Teme'im), the following Teme'im may not eat it: a Zav, Metzora, Zavah or Yoledes.

Beis Hillel: Korban Pesach is different. There the Torah permitted only "Tamei la'Nefesh" (Tum'as Mes);

Regarding Bechor, it permits "Tamei" without distinction.

(Beraisa): On Yom Tov one may not be Margil (flay an animal from the legs, in order to keep the skin whole, in order to make a bellows or pouch);

Similarly, one may not be Margil a Bechor or Pesulei ha'Mukdashim.

Question: We understand why it is forbidden on Yom Tov. Even though one may flay in order to eat on Yom Tov, flaying in this way is an exertion not needed for Yom Tov;

However, which Tana forbids Hargalah of a Bechor?

Answer (Rav Chisda): It is Beis Shamai, who forbid Bechor to a Nidah (because it retains its Kedushah, even after Shechitah).

Question: Which Tana forbids Hargalah of Pesulei ha'Mukdashim?

Answer (Rav Chisda): It is R. Elazar b'Rebbi Shimon (who holds that it retains its Kedushah, even after Shechitah):

(Beraisa): If Reuven designated two animals for Acharayus for his Chatas (in case one will be lost, he will offer the other), and one of them became a Ba'al Mum:

He offers the Tam, and redeems the Ba'al Mum. (The money is used for Nidvos Tzibur, voluntary offerings when the Mizbe'ach is idle);

If (after Pidyon) the Ba'al Mum was slaughtered before Zerikas Dam of the Tam, it is permitted;

If the Ba'al Mum was slaughtered after Zerikah, it is forbidden;

R. Elazar b'Rebbi Shimon says, even if the meat of the Ba'al Mum was in a bowl and Zerikah (of the Tam) was done, it is forbidden.

Question: Why didn't Rav Chisda establish the entire Mishnah to be like Beis Shamai?

Answer: Perhaps Beis Shamai hold that only Bechor retains its Kedushah, for it is Kodesh from birth, but other Pesulei ha'Mukdashim do not.

Question: Why didn't Rav Chisda establish the entire Mishnah to be like R. Elazar b'Rebbi Shimon?

Answer: Perhaps R. Elazar b'Rebbi Shimon holds that Pesulei ha'Mukdashim retain their Kedushah after Shechitah, for their Kedushah is strong enough to be Matpis Pidyonam;

The Kedushah of Bechor is too weak to be Matpis Pidyono, so it does not retain its Kedushah after Shechitah.

Question: Does R. Elazar argue with our Mishnah, which permits selling Pesulei ha'Mukdashim in an Itliz and by weight?

The Mishnah allows a disgrace to Hekdesh for the sake of a monetary gain to Hekdesh. R. Elazar forbids Hargalah, even though it increases the redemption value!

Answer #1 (Rav Mari brei d'Rav Kahana): R. Elazar could agree with our Mishnah. Hargalah increases the value of the skin, but not the total (redemption) value (Rashi - very much), for it cuts the meat, and decreases its value.

Answer #2 (Chachamim of Eretz Yisrael): R. Elazar could agree with our Mishnah. Hargalah is forbidden for it is a big disgrace. It looks like working with Kodshim. (He flays for the sake of the skin, not in order to eat.)

Answer #3 (R. Yosi bar Avin): He could agree with our Mishnah. He decrees to forbid Hargalah, lest one delay slaughtering Pesulei ha'Mukdashim (until finding one who wants to buy the skin), and grow herds of them. (Perhaps he will come to shear or work them.)

(Mishnah - R. Yehudah): If a Bechor is sick due to excess blood, even if it will die, one may not let blood;

Chachamim permit letting blood, as long as he does not (expect to) make a Mum;

If a Mum was made, one may not slaughter it (outside the Mikdash) until it gets another Mum.

R. Shimon permits letting blood, even if this will make a Mum.

(Gemara - Beraisa - R. Meir): If a Bechor is sick due to excess blood, one may let blood, but only in a place that will not make a Mum;

Chachamim permit even in a place that will make a Mum, but one may not slaughter it until it gets another Mum;

R. Shimon permits relying on that Mum to slaughter it;

R. Yehudah says, even if it will die, one may not let blood.

(R. Elazar): The argument about bloodletting is like the argument about Terumah:

(Mishnah): If Terumah became doubtfully Tamei:

R. Eliezer says, if it was in an open place (prone to become definitely Tamei), we put it in a hidden place. If it was exposed, we cover it;

R. Yehoshua says, if it was in a hidden place, we put it in an open place. If it was covered, we expose it. (We want it to become definitely Tamei, for then it may be used. E.g. a Kohen may benefit from burning it, or he may spray wine on the floor to give a nice aroma.)

R. Gamliel says, we leave it like it is.

R. Meir holds like R. Eliezer, Chachamim hold like R. Yehoshua, and R. Yehudah holds like R. Gamliel.

Rejection #1: This is not necessarily true!

R. Meir forbids overtly making a Mum. Perhaps he would permit causing Tum'ah, like R. Yehoshua;

R. Eliezer requires guarding Safek Terumah from definite Tum'ah. Perhaps this is because we anticipate that Eliyahu will come soon, and he will tell us that it is really Tahor. However, R. Eliezer would permit letting blood from a Bechor like Chachamim, lest it die!

Chachamim permit letting blood, lest it die. Perhaps they require guarding the Terumah like R. Eliezer, for Eliyahu might tell us that it is Tahor!

R. Yehudah forbids overtly making a Mum. Perhaps he would permit causing Tum'ah, like R. Yehoshua.

R. Gamliel forbids changing its status. Perhaps this is because we anticipate Eliyahu, but he would permit letting blood, lest the Bechor die!

Rejection #2: (Regarding Bechor) the Tana'im argue about a verse:

(R. Chiya bar Aba): (Regarding Menachos,) all agree that one is liable for Mechametz (fermenting) after Mechametz. It says "Lo Se'aseh Chametz" and "Lo Se'afeh Chametz" (to make a person liable for every step);

All agree that one is liable for Mesares (castrating) after Mesares. It says "u'Ma'uch v'Chasus v'Nasuk v'Charus" (the verse discusses Mumim of castration. It ends "... uv'Artzechem Lo Sa'asu");

Question: If one is liable for Kores (disconnecting the testicles), all the more so for Nosek (Tosfos - totally cutting them off, but they are still in the sac; Rashi - removing them from the sac). Why did the Torah need to say "v'Nasuk"?

Answer: This obligates for Nosek after Kores.

They argue only about making a Mum in a Ba'al Mum;

R. Meir is Mechayev due to "Kol Mum Lo Yihyeh Bo";

Chachamim exempt. It says "Tamim Yihyeh l'Ratzon." (Since a Ba'al Mum cannot be (offered) l'Ratzon, the Lav of making a Mum does not apply.)

Question: How does R. Meir expound Chachamim's verse?

Answer #1: It excludes a Ba'al Mum me'Ikaro. (It was blemished before it became Kodesh.)

Rejection: Such an animal was never Kosher to be offered. Obviously the Lav does not apply!

Answer #2: Rather, it excludes Pesulei ha'Mukdashim after Pidyon:

Since one may not work with or shear them, one might have thought that also the Isur to blemish them remains. The verse teaches that this is not so.

Question: How do Chachamim expound R. Meir's verse?

Answer: It forbids causing a Mum:

(Beraisa): We read "Kol Mum Lo Yihyeh Bo" like "(Lo) Yehayei" (do not directly cause - Tosfos Yom Tov; Rashash - "(Lo) Yehayeh" there shall not be) a Mum;

Question: What is the source to forbid causing a Mum, e.g. sticking food to the ear (inciting dogs to eat the food, and thereby cut the ear)?

Answer: It could have said only "Mum". "Kol Mum" is extra, to equate making a Mum and causing a Mum.