Pesachim 60B

אלא לאו: בעבודה אחת, ומדסיפא בעבודה אחת ⁠— רישא נמי בעבודה אחת!

Rather, doesn’t it refer to a case in which one had both intentions during one rite, and nevertheless it is valid? And since the latter clause speaks about one rite, the first clause, the current Mishnah, must also speak about one rite, and yet the offering is disqualified, because even the conclusion of one’s statement is significant, in accordance with the opinion of R' Yosei.

מידי איריא?! הא כדאיתא והא כדאיתא. סיפא בעבודה אחת, ורישא או בעבודה אחת, או בשתי עבודות.

The Talmud refutes this proof as it refuted the previous one: Are the two cases comparable? Perhaps this case is as it is and that case is as it is. There is no reason to equate the cases, as it is possible to say that the latter clause speaks about one rite, whereas the first clause, the current Mishnah, speaks either about one rite or about two rites. Therefore, there is no conclusive resolution to Rav Pappa’s question.

איבעיא להו: פסח ששחטו בשאר ימות השנה לשמו ושלא לשמו, מהו? מי אתי שלא לשמו ומפיק ליה מידי לשמו ומכשיר ליה, או לא?

A dilemma was raised before the rabbis: A Paschal lamb that one slaughtered on the rest of the days of the year other than the eve of Passover for its own purpose and for a different purpose, what is its status? The Talmud clarifies the two sides of the issue: Does the intent to offer the sacrifice for a different purpose come and nullify the intent to offer the sacrifice for its own purpose and thereby make it valid, or not? The law is that a Paschal lamb that was slaughtered for a different purpose at a time other than Passover eve attains the status of a peace-offering and is therefore valid. The question raised here is whether or not partial intent to slaughter the animal as a peace-offering rather than as a Paschal lamb suffices to validate the offering.