Pesachim 78B

הא אמרת, בציבור אפילו רבי יהושע מודה.

Didn’t you say that with regard to an offering involving the public, even R' Yehoshua concedes that ritual impurity is permitted?

אלא: רואה אני דברי רבי אליעזר בדיעבד, ודברי רבי יהושע לכתחלה. דיעבד ⁠— אפילו רבי יהושע נמי מודה הוא, דקתני: מודה רבי יהושע שאם זרק ⁠— הורצה!

Rather, R' Yosei’s statement should be understood differently. When he said: I see as correct the statement of R' Eliezer, he was referring to after the fact. When he said: I see as correct the statement of R' Yehoshua, he meant ab initio. The Talmud asks: After the fact R' Yehoshua also concedes, as it teaches: R' Yehoshua concedes that if one sprinkled the blood, it was accepted and the offering is valid.

הא בטומאה, הא באבוד ושרוף. כי קתני: מודה רבי יהושע שאם זרק הורצה ⁠— בנטמא, אבל באבוד ושרוף לא. כי קאמר רבי יוסי: רואה אני את דברי רבי אליעזר בדיעבד ⁠— באבוד ושרוף.

The Talmud responds: This case is with regard to ritual impurity, and that case is with regard to an offering that was lost or burned. The Talmud explains: When it teaches that R' Yehoshua concedes that if one sprinkled the blood it is accepted, that is with regard to a case in which the meat of the offering became impure; but with regard to a case where the meat of the offering was lost or burned, he does not agree, even after the fact. When R' Yosei said: I see as correct the opinion of R' Eliezer after the fact, that was with regard to cases in which the meat was lost or burned, with regard to which R' Yehoshua did not concede to R' Eliezer.

מתני׳ נטמא בשר וחלב קיים ⁠— אינו זורק את הדם. נטמא החלב והבשר קיים ⁠— זורק את הדם. ובמוקדשים אינו כן, אלא אף על פי שנטמא הבשר והחלב קיים ⁠— זורק את הדם.

Mishnah: If the meat of the Paschal lamb became ritually impure, and the fat remains pure and may be burned on the altar, one may not sprinkle the blood. On the other hand, if the fat became impure and the meat remains pure, one may sprinkle the blood because the meat remains fit to be eaten. This is the halakha with regard to a Paschal lamb, whose primary purpose is to be eaten by those who have registered for it. However, with regard to other offerings it is not so. Rather, although the meat has become impure and the fat remains pure, one may sprinkle the blood, because part of the offering still remains valid.