(Mishnah - R. Chanina Segan ha'Kohanim): Kohanim never refrained from burning [Kodesh] meat that became Tamei through a Vlad ha'Tum'ah with meat that became Tamei through an Av ha'Tum'ah, even though this increases the Tum'ah of the former meat (this will be explained; also, see note 13 in Appendix);

R. Akiva taught further - Kohanim never refrained from burning [Kodesh] oil that became Tamei through a Tevul Yom (someone who was Tamei and immersed today; he remains slightly Tamei until nightfall) in a lamp that became Tamei through a Tamei Mes, even though this increases its Tum'ah (this will be explained).

R. Meir says, we learn from their words that one may burn Tahor Terumah [of Chametz] together with Tamei Terumah [at the time of Bi'ur] on [Erev] Pesach even though this is Metamei it [since it had to be burned anyway].

R. Yosi: We may not learn this! R. Eliezer and R. Yehoshua agree that each is burned by itself - they argue about Taluy and Tamei Terumah:

R. Eliezer says that each is burned by itself; R. Yehoshua permits burning them together.

(Gemara) Question: Meat that became Tamei through an Av is a Rishon l'Tum'ah; meat that became Tamei through a Vlad is a Sheni - [why did R. Chanina say that burning them together increases the Tum'ah,] a Rishon only makes a Sheni!

Answer (Rav Yehudah): The case is, the latter meat touched a Sheni, it is only a Shelishi - R. Chanina permits [burning it with a Rishon and] making it a Sheni.

Question: Food does not Metamei food!

(Beraisa) Suggestion: Perhaps food is Metamei food!

Rejection "V'Chi Yutan Mayim Al Zera v'Nofal mi'Nivlasam Alav Tamei Hu" - it (food) is Tamei, but it is not Metamei [other food] like itself.

Answer #1: According to Abaye, the Beraisa discusses Chulin, but Terumah and Kodshim are Metamei [other foods] like themselves.

Answer #2: According to Rav Ada bar Ahavah in the name of Rava, the Beraisa discusses Chulin and Terumah, but Kodshim are Metamei like themselves.

Question: However, Ravina says in the name of Rava that the verse applies to everything - Chulin, Terumah, and Kodshim do not Metamei like themselves - how can he answer?

Answer #3: The case is, there are liquids with the meat - the liquids Metamei the meat.

Objection: If so, why does it say that they would burn 'with meat that became Tamei through an Av ha'Tum'ah' - it should say 'with meat and liquids'!

Answer #4: Food does not Metamei food mid'Oraisa, but mid'Rabanan it does.

(Mishnah): R. Akiva taught further - Kohanim never refrained...

Question: Oil that became Tamei through a Tevul Yom is a Shelishi; when it is burned in a lamp that became Tamei through a Tamei Mes (a Rishon), the oil becomes a Sheni - this is just like R. Chanina taught (why does it say 'R. Akiva taught further'?! This is not difficult according to Answer #4, for R. Chanina discusses [increasing Tum'ah] mid'Rabanan, and R. Akiva discusses mid'Oraisa).

Answer (Rav Yehudah): That Mishnah discusses a metal lamp;

It says "Ba'Chalal Cherev" -a sword [or anything else metal that touched a corpse] becomes like a Mes (Avi Avos ha'Tum'ah, i.e. it can make an Av ha'Tum'ah - likewise), the lamp becomes [like the Tamei Mes it touched;] an Av ha'Tum'ah;

R. Akiva permits to Metamei a Shelishi and make it a Rishon.

Question: What forced Rav Yehudah to say that it discusses a metal lamp? He could have said that it is Cheres - R. Chanina only permitted increasing Tum'ah of something already Tamei (it can Metamei other things), and R. Akiva permits to make Tamei something that was only Pasul (disqualified, but it could not Metamei anything else)!

Answer (Rava) Question: Why does the Mishnah say that the lamp became Tamei through a Tamei Mes? It could have said that it touched a Sheretz (dead rodent, a lighter Tum'ah)!

Answer: This shows that it discusses a lamp which receives a different Tum'ah from a Tamei Mes than from a Sheretz, i.e. a metal lamp (it becomes an Av ha'Tum'ah through a Tamei Mes).

Inference (Rava): This shows that R. Akiva holds that mid'Oraisa, liquids can Metamei other things;

If it was Metamei only mid'Rabanan, the lamp did not change anything - the oil was already Pasul [and still it cannot Metamei mid'Oraisa]!

Question: [Perhaps it is not mid'Oraisa -] the lamp enables the oil to Metamei other things mid'Rabanan!

Answer: If so, the Mishnah would not have had to say that the lamp was an Av ha'Tum'ah - even if it was a Rishon or Sheni, it would make the oil a Rishon [mid'Rabanan, which can Metamei]!

(Mishnah): The only Tum'ah that is Posel Terumah but does not make a liquid a Rishon is a Tevul Yom.

Conclusion: He holds that liquids can Metamei mid'Oraisa.

(Mishnah - R. Meir): We learn from their words...[that one may burn Tahor and Tamei Terumah together].

Question: From whom do we learn this?

Answer #1: We learn from R. Chanina.

Rejection: R. Chanina only permitted increasing Tum'ah of something already Tamei - R. Meir permits to Metamei something Tahor!

Answer #2: We learn from R. Akiva.

Rejection: R. Akiva only permitted to Metamei something Pasul - R. Meir permits to Metamei something Tahor!

Suggestion: R. Meir holds that the Mishnah discusses an Av ha'Tum'ah mid'Oraisa and a Vlad ha'Tum'ah mid'Rabanan - mid'Oraisa, the meat was Tahor; we learn from R. Chanina [that we may burn in the sixth hour, when Chametz is permitted mid'Oraisa and forbidden mid'Rabanan].