The Mishnah (9:8) discusses cases where a korban Pesach was mixed with other korbanot. One case highlighted is where a korban Pesach was mixed with bechorot. The Mishnah cites the opinion of R’ Shimon who explains that if the chaburah - the individuals part of the korban pesach – were all kohanim, then all the korbanot may be offered and then consumed that evening.
An unblemished bechor (kosher, first-born animal) must be brought to Yerushalaim and offered as a korban. The parts that can be consumed are only permissible to the kohanim. The requirements and manner in which both korbanot are offered is the same. One important difference is that one only has until midnight to consume the korban pesach, whereas the kohanim can consume the bechor that day, night and following day.
The Bartenura explains that despite the fact that if the entire mixture is offered one will effectively be reducing the amount of time that the bechor (in the mixture) can be consumed, R’ Shimon is not bothered. The Chachamim however are. They maintain that the mixture must be treated like any other mixture of a korban pesach and other korbanot. The animals must all be left until they develop blemishes that invalidate them from being used as korbanot. The korban pesach must then be redeemed and a new animal purchased, with a value equal to the most expensive animal from the original mixture. (Unlike other korbanot, once a bechor develops a mum it does not need to be redeemed and is given to a kohen.)
The Tosfot (Yoma 29a) however are bothered. We have learnt that the korban pesach was offered after the korban tamid. Furthermore, no korban other than the korban pesach can be offered after the korban tamid. Doing so would violate the positive mitzvah of hashlama. According to R’ Shimon, when was the mixture of korbanot offered?
The Sefat Emet answers that the mixture was slaughtered after midday, but prior to the korban tamid. Even though, ideally the korban pesach should be offered after the korban tamid, the korban is nonetheless valid (see 5:3, and Vol. 14, Iss. 20). He explains that offering the mixture in this manner is preferable to offering the mixture after the korban tamid which would then violate the positive mitzvah.
The Tifferet Yisrael explains similarly that the entire mixture would be slaughter. The blood from the korbanot however would be stirred in order that they could be thrown on the mizbeach after the blood of the korban tamid. Recall that this consistent with the earlier Mishnah (8:3) that if the korban pesach was slaughtered before the korban tamid, that the blood should still be thrown on the mizbeach after the blood of the korban tamid.
The Sefat Emet however asks why the Mishnah did not select a simpler case with a broader scope. Consider the case of a mixture of maaser beheima and a korban pesach. Maaser beheima refers to every tenth new-born (kosher) animal, that must be offered as a korban. Its requirements and way it is offered is the same as the bechor, yet it is consumed by the owners – even non-kohanim. In that case, R’ Shimon would rule that the entire mixture could be offered and consumed by the members of the chaburah, even if the chaburah consisted of non-kohanim.
The Tifferet Yisrael answers, that it was important to teach the case of the mixture including bechorot. One might have thought that in that case R’ Shimon would agree with the Chachamim out of concern that one would mistakenly apply the same rule for such a mixture where the chaburah included people who were not kohanim.
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