Beis Shammai: One cannot bring challah and matnos kehunah to a kohen on Yom Tov whether it was separated before Yom Tov or on Yom Tov. Beis Hillel permit it.
The Gemara explains that since it seems there is no situation in which Beis Shammai would permit bringing mattanos on Yom Tov, our Mishnah must be said according to Acherim and not Rabbi Yehuda or Rabbi Yosi.
Rabbi Yehuda: Mattanos separated before Yom Tov may be brought on Yom Tov together with mattanos separated on Yom Tov.

Beraisa (continued): Rabbi Yosi: Beis Shammai and Beis Hillel agree that mattanos may be taken to the kohen on Yom Tov, their debate is only regarding Terumah.
Acherim: Beis Shammai and Beis Hillel agree that terumah may be taken to the kohen on Yom Tov, their debate is only regarding Mattanos.

So it seems that our Mishnah follows only Acherim and not Rabbi Yehuda? [We always like to explain a Mishnah according to more Tannaim and not limit it only to one opinion. Rabbi Yosi’s opinion is clearly irreconcilable with the Mishnah since according to him Beis Hillel permit bringing Terumah, but we’re attempting to make the mishnah work according to Rabbi Yehuda].

Rava: The Mishnah is discussing an animal slaughtered before Yom Tov, Rabbi Yehuda is discussing an animal slaughtered on Yom Tov. [They can thus be in agreement].

Question: Is the Mishnah then only in accordance with Rabbi Yehuda and not with Acherim?

Response: Acherim also agree that mattanos of animals slaughtered on Yom Tov can be brought on Yom Tov.

Challenge: If so, in what area does he differ with Rabbi Yehuda?Resolution: Only Rabbi Yehuda permits bringing yesterday’s, when it is brought together with today’s. 

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