"Lecha Hu" teaches that the money of Gezel ha'Ger (if one stole from a convert, swore to deny it, and repents after the convert died without heirs, he gives the money to a Kohen) belongs to the Kohen. He may use it like he wants. He may even be Mekadesh a woman with it.

Bava Kama 12b (Beraisa - R. Yosi ha'Glili): "He transgressed in Hash-m (and denied his fellowman)" includes Kodshim Kalim, which (pertain to Hash-m and) are (also) Mamon Ba'alim (the owner's property).

(Mishnah): If one was Mekadesh with his portion of Kodshim, whether Kodshei Kodoshim or Kodshim Kalim, the Kidushin is invalid.

This can even be like R. Yosi ha'Glili. He said that Kodshim Kalim are Mamon Ba'alim only in the life of the animal. After Shechitah, he agrees that they are considered Hash-m's, just we may eat them.

Question: Does R. Yosi ha'Glili really hold that Kodshim Kalim are Mamon Ba'alim in the life of the animal?!

(Mishnah): A Tam (unblemished) Bechor (male firstborn animal) may be sold when alive. If it is blemished, it may be sold alive or slaughtered. He (the Kohen) may use it to be Mekadesh a woman.

(Rav Nachman): This is only nowadays. Since it cannot be offered, Kohanim own it. When the Mikdash stands, Kohanim do not own it.

Question (Rava - Beraisa - R. Yosi ha'Glili): "U'Ma'al Ma'al ba'Hashem" includes Kodshim Kalim, which are Mamon Ba'alim.

Answer (Ravina): The Beraisa discusses a Bechor in Chutz la'Aretz, according to R. Shimon. He holds that if they were brought to the Mikdash Tam, they are offered. L'Chatchilah, we do not bring them.

(Summation of question): If R. Yosi ha'Glili holds that they are Mamon Ba'alim while they are alive, Ravina should rather have answered that the Beraisa is R. Yosi, and Rav Nachman's law is like Chachamim!

Answer: Gifts to the Kohen are unlike other Kodshim Kalim. They are Hash-m's (just the Kohen may eat them).

53b (Abaye): If Reuven's ox and a blemished Korban gored together, Reuven pays half-damage;

(Ravina): He pays quarter-damage.

Ravina discusses a Tam, according to Chachamim (who hold that one does not collect from one damager what cannot be collected from another damager). Abaye discusses a Mu'ad, or a Tam according to R. Nasan, who argues with Chachamim.

Zevachim 114a: Question: If an animal was Ne'evad or Muktzeh (worshipped or designated for worship), since no action was not done to the animal itself, only the owner can forbid it. Once it is Hekdesh, he ceases to own it!

Answer: Our Mishnah discusses Kodshim Kalim. It is like R. Yosi ha'Galili, who says that Kodshim Kalim are considered Mamon Ba'alim.

Chulin 36b: "(Kodesh) meat that will touch anything Tamei (may not be eaten)" teaches that meat of Korbanos become Huchsher (susceptible to receive Tum'ah) due to Chibas (the dearness of) ha'Kodesh.

Rejection: Perhaps the Hechsher was like Rav Yehudah said. A Shelamim was taken through a river, and it was still wet when it was slaughtered.

Rambam (Hilchos Nizkei Mamon 8:1): If a person's ox gored a Hekdesh ox or vice-versa, it is exempt. Payment of damage does not apply to any Hekdesh to which Me'ilah applies.

Lechem Mishneh: This is like R. Yosi ha'Glili, who holds that there is Hekdesh to which Me'ilah does not apply, i.e. Kodshim Kalim. They are Mamon Ba'alim, so payments for damage apply to them.

Support (Ketzos ha'Choshen 406:1): We say (Chulin 36a) that perhaps a Shelamim was taken through a river, and it was still wet when it was slaughtered, and this was Machshir it. The Rambam (Hilchos Tum'as Ochlim 12:1) says that Hechsher requires the owner's consent that it become wet. On 114a, the only way we find that someone owns a Korban is Kodshim Kalim, according to R. Yosi. This explains why Rav Yehudah mentioned a Shelamim (it is Kodshim Kalim).

Rosh (Bava Kama 1:15): We conclude that R. Yosi ha'Glili agrees that when the Mikdash stands, Matanos Kehunah are not Mamon Ba'alim. However, nowadays a Bechor is Mamon Ba'alim and can be used to be Mekadesh a woman even if it is Tam. Rabanan hold that even a live Ba'al Mum is not Mamon Ba'alim, like we say on 53b. Rav Yehudai Ga'on explains that Abaye and Ravina discuss a Bechor ox, which cannot be redeemed. Presumably, they argued about the Halachah in their days (after the Churban). This (its exemption for damage) shows that it is not Mamon Ba'alim, for one may not shear it or work with it or (regarding other blemished Korbanos) milk it. Some rule like R. Yosi ha'Glili, for the Stam Mishnah is like him. Rava established the Mishnah like Chachamim, but he retracted due to a question against himself. However, it seems to me that the Halachah follows Chachamim, since Abaye and Ravina argue about according to Chachamim, and they are Basra. If so, if a Kohen was Mekadesh with a live Bechor, she is not Mekudeshes. This requires investigation.

Rosh (Bechoros 5:1): A Mishnah teaches that one may sell a Bechor Tam when alive, and blemished alive or slaughtered. He may use it to be Mekadesh a woman. Rav Nachman said that this is nowadays, when it cannot be offered, so Kohanim own it.

Yam Shel Shlomo (Bava Kama 1:34): Our Mishnah is like R. Yosi ha'Glili. He admits about Matanos Kehunah, including Bechor at the time of the Mikdash. It is not Mamon Ba'alim; Kohanim receive their portion from Hash-m. It is improper to be Mekadesh a woman with it, and it is like Hekdesh regarding damage. Nowadays, even if it is Tam, it is Mamon Ba'alim to be Mekadesh a woman and everything. The Halachah follows R. Yosi, for the Mishnah is like him. The Rosh brought a proof from 53b. I disagree. Abaye and Ravina just show different laws based on R. Noson's law. In one version there, both teach according to Chachamim, even though the Halachah follows R. Noson. Likewise, even though the Halachah follows R. Yosi, they discuss the law according to Chachamim. This is relevant to us (who rule like R. Yosi) nowadays, regarding a Hekdesh ox. Also, even though the Halachah always follows Chachamim, even when they argue with Tana'im whom the Halachah normally follows, such as R. Noson, who was a judge, his words are Batel against Chachamim. Even so, the Rif rules like him because scrutiny shows that the Mishnah is like him. Similarly, scrutiny shows that the Mishnah is like R. Yosi, even though Chachamim disagree. Whenever the Beraisa of R. Yosi ha'Glili is brought, only his opinion is cited. This shows that his opinion is primary. I say that the Rosh retracted. In Bechoros he brings the Mishnah to be the Halachah, and here he says 'this requires investigation.' Therefore, nowadays Kidushin with a live Bechor Tam, or a Ba'al Mum live or slaughtered, is Mekudeshes mid'Oraisa.

Rashi (12b DH u'Mekadshin): The Kohen can be Mekadesh with a Bechor. He is the owner from when it is born.

Shulchan Aruch (YD 306:6): Nowadays, a Kohen may sell a Bechor even to a Yisrael when it is Tam (unblemished) and alive, or when it has a Mum alive or slaughtered. He can be Mekadesh a woman with it, for it is like any of his property.

Shulchan Aruch (EH 28:23): Nowadays, if the owner of a Bechor was Mekadesh a woman with it, she is Safek Mekudeshes.

Chelkas Mechokek (43): Stam, the Kohen is the owner of a Bechor, like Rashi says. This is from the Mishnah that permits selling a Bechor or being Mekadesh with it. The Shulchan Aruch rules like this in YD. Here the Shulchan Aruch says that she is Safek Mekudeshes, like the Rosh in Bava Kama. Also the Rosh contradicts himself. In Bechoros, he rules like the Mishnah without Safek. Even in Bava Kama the Rosh was unsure only about a live Bechor, for one may not shear or work it. A slaughtered Ba'al Mum is Mamon Ba'alim in every way. One may feed it even to a Nochri or dog. All the more so one may be Mekadesh a woman with it.

Beis Shmuel (60): Nowadays, Kidushin with a live Bechor is a Safek, but after a Ba'al Mum was slaughtered, all agree that it is the Kohen's money. In YD, the Shulchan Aruch says that one can be Mekadesh a woman with it, i.e. after Shechitah, which was the last case discussed there.

Gra (61): Abaye and Rava (it seems that this should say 'Ravina' - PF) argue about according to Chachamim (of R. Yosi), i.e. about a live Bechor. What the Shulchan Aruch wrote in YD is primary.