The Gemara responds: Yes, it can be explained that the first clause is referring to two sacrificial rites, while the latter clause, i.e., the disagreement between Rabbi Yehuda and the Rabbis, applies to both one rite and two rites.

The Gemara suggests a proof: We learned in the mishna: Rabbi Yehuda says that this is the principle: If the intent with regard to the time preceded the intent with regard to the area, the offering is piggul and one is liable to receive karet for burning or partaking of it. Granted, according to Rabbi Yoḥanan, who says that the disagreement applies even to one rite, this is the reason that the tanna teaches: This is the principle, indicating that the principle is broad. But according to Ilfa, what is added by the phrase: This is the principle? The Gemara responds: This indeed poses a difficulty to the opinion of Ilfa.

§ We learned in a mishna elsewhere (Temura 25b): If one had two animals standing before him, one a burnt offering and one a peace offering, and he said with regard to another non-sacred animal of his: This animal is hereby the substitute of the burnt offering, the substitute of the peace offering, then that animal is the substitute of the burnt offering; this is the statement of Rabbi Meir.

Rabbi Yosei said: If that was his intent from the outset, i.e., his intent was that this animal be the substitute of both a burnt offering and a peace offering, since it is impossible to produce two designations simultaneously and one designation must precede the other, his statement is effective, and the animal is the substitute of both a burnt offering and a peace offering. But if it was only after he said: This animal is hereby the substitute of the burnt offering, that he reconsidered and said: This animal is hereby the substitute of the peace offering, then that animal is the substitute of a burnt offering alone.

A dilemma was raised before the Sages: If one expressed the two intentions simultaneously and said: This is hereby the substitute of a burnt offering and a peace offering, what is the halakha? Additionally, if one specified his intention to split the animal between a burnt offering and a peace offering, but mentioned the burnt offering first, what is the halakha?

Abaye said: In this case, Rabbi Meir certainly concedes that both types of sanctity apply to the animal. Rava said: It is still a disagreement; Rabbi Meir still holds in this case that since he mentioned the burnt offering first, only that sanctity applies to the animal.

Rava said to Abaye: According to your opinion, as you say that in this case Rabbi Meir certainly concedes, one may raise an objection from the mishna, which describes a case where one performs slaughter with intent to eat one olive-bulk of the offering beyond its time and one olive-bulk outside its area, which is comparable to a case where one says: To split, since both intentions are held during the singular act of slaughter. And nevertheless, Rabbi Yehuda and the Rabbis disagree, and Rabbi Yehuda, who holds that one attends only to the first statement, renders the animal piggul.

Abaye said to him: Do you hold that slaughter is considered to have been performed only at its end, such that it takes effect in a single instant? Actually, slaughter is accomplished progressively, from beginning to end, and our mishna is referring to a case where one says: I slaughter the first siman, the gullet or the windpipe, with intent to consume the offering beyond its designated time, and the second siman with intent to consume it outside its designated area.

The Gemara asks: But what about the removal of a handful from a meal offering with intent to eat one olive-bulk beyond its time and one outside of its area, which is comparable to a case where one says: To split, since both intentions are held during the removal, and nevertheless, Rabbi Yehuda and the Rabbis disagree with regard to it in tractate Menaḥot (12a)?

The Gemara responds: Since the mishna does not state such a dispute explicitly, one can say that their disagreement is not with regard to the removal of the handful but with regard to the burning of the two permitting factors of the meal offering, the handful and the frankincense. Accordingly, there too, the case is such that the priest burned the handful of the meal offering with intent to eat it beyond its designated time, and he burned the handful of frankincense with intent to eat the meal offering outside its designated area.

The Gemara persists: But what about the handful from a meal offering of a sinner, which has no frankincense with it, and still Rabbi Yehuda and the Rabbis disagree?

The Gemara responds: In that case they do not disagree. Rav Ashi says: Even if you say that they disagree in that case, one may say that they disagree specifically with regard to a case where the priest had different intentions during his steps toward the altar while holding the handful. Consequently, even this rite is divisible into separate parts.

Rav Shimi bar Ashi would teach in accordance with the opinion of Abaye that in a case where one explicitly mentions both intentions at once, Rabbi Meir concedes that both sanctities apply to the animal. Rav Huna bar Natan would teach in accordance with the opinion of Rava that even in such a case, Rabbi Meir considers only the first sanctity mentioned.

When Rav Dimi came from Eretz Yisrael to Babylonia, he said: When Rabbi Meir said that if one says: This animal is hereby the substitute of a burnt offering, the substitute of a peace offering, then the animal is the substitute of a burnt offering, he said this according to the opinion of Rabbi Yehuda, who says that in general, the halakha is to attend only to the first statement.

As we learned in the mishna: Rabbi Yehuda said that this is the principle: If the intent with regard to the time preceded the intent with regard to the area, the offering is piggul and one is liable to receive karet for burning or partaking of it.