Mishnah Zevachim 1:2:Yose ben Choni says: Those [animals] which are slaughtered for the sake of a Passover offering and for the sake of a Chattat are invalid. Shimon Achi Azariah says: if they were slaughtered for the sake of a higher-level offering they are valid; for the sake of a lower-level offering they are invalid. How so? Kodshai Kodashim [sacrifices of the highest degree of sanctity. They may be slaughtered only on the north-west corner of the altar, and consumed only within the Temple compound by male priests, or burnt entirely] that were slaughtered for the sake of Kodashim Kalim [sacrifices of a lesser degree of sanctity. They may be slaughtered anywhere in the Temple courtyard and consumed by most anyone, anywhere in Jerusalem] are invalid. Kodashim Kalim that were slaughtered for the sake of Kodshai Kodashim are valid. The Bechor [first-born offering] or a Ma'aser [animal tithe] that were slaughtered for the sake of a Shelamim [an offering whose various parts are consumed by its owners, the Kohanim and the fire on the altar] are valid. And Shelamim that were slaughtered for the sake of a Bechor or for the sake of Ma'aser are invalid.

יוסי בן חוני אומר: הנשחטים לשם פסח ולשם חטאת, פסולים. שמעון אחי עזריה אומר: שחטן לשם גבוה מהם, כשרין. לשם נמוך מהם, פסולים. כיצד, קדשי קדשים ששחטן לשם קדשים קלים, פסולין, קדשים קלים ששחטן לשם קדשי קדשים, כשרין. הבכור והמעשר ששחטן לשם שלמים כשרין, ושלמים ששחטן לשם בכור, לשם מעשר, פסולין.

Mishnah Zevachim 1:3: [If] a Passover offering was slaughtered in the morning of the fourteenth [of Nisan, but not for its own sake, Rabbi Yehoshua deems it valid, as if it had been slaughtered on the thirteenth [of Nisan]. Ben Beteira invalidates it, as if it had been slaughtered in the afternoon. Shimon ben Azzai said: I received a tradition from the mouths of seventy-two elders on the day they appointed Rabbi Eliezer ben Azariah as [head of the] academy, that all offerings that are eaten which were not slaughtered for their own sake are valid, but they have not fulfilled the obligations of [their] owners. [This is true] except for the Passover offering and the Chattat. And Ben Azzai did not add [to this tradition] except [to include] the burnt-offering, but the sages did not agree with him.

הפסח ששחטו בשחרית בארבעה עשר שלא לשמו, רבי יהושע מכשיר, כאלו נשחט בשלשה עשר. בן בתירא פוסל, כאלו נשחט בין הערבים. אמר שמעון בן עזאי: מקבל אני מפי שבעים ושנים זקן ביום שהושיבו רבי אלעזר בן עזריה בישיבה, שכל הזבחים הנאכלים שנזבחו שלא לשמן, כשרים, אלא שלא עלו לבעלים משום חובה, חוץ מן הפסח ומן החטאת. ולא הוסיף בן עזאי אלא העולה, ולא הודו לו חכמים.