Zevachim 16A

זר, שאינו אוכל ⁠– אינו דין שאם עבד חילל?!

then with regard to a non-priest, who may not partake of the meat of offerings of the most sacred order, is it not right that if he performed sacrificial rites he has desecrated the service?

מה לבעל מום ⁠– שכן עשה בו קרב כמקריב!

The Talmud rejects the inference: One cannot draw an a fortiori inference from a blemished priest, as what is notable about the case of a blemished priest? It is notable in that the Torah rendered an animal that is sacrificed like the priest who sacrifices it, i.e., both blemished animals and blemished priests are disqualified. Since there is an added element of stringency with regard to the case of a blemished priest, one cannot draw an a fortiori inference from it.

טמא יוכיח. מה לטמא ⁠– שכן מטמא!

The Talmud suggests: The case of an impure priest will prove that this is no reason to reject the a fortiori inference. While an animal and the priest are not equated with regard to ritual impurity, as an animal cannot become impure while alive but a priest can, an impure priest desecrates the service. The Talmud rejects this as well: What is notable about the case of an impure priest? It is notable in that an impure priest imparts impurity to others.

בעל מום יוכיח. וחזר הדין. לא ראי זה כראי זה, ולא ראי זה כראי זה; הצד השוה שבהן ⁠– שמוזהרין, ואם עבדו חיללו; אף אני אביא זר ⁠– שהוא מוזהר, ואם עבד חילל.

The Talmud responds: A blemished priest will prove that this is no reason to reject the inference, as he cannot impart his blemish to others. And the inference has reverted to its starting point. Therefore, one may derive the halakha of a non-priest from the combination of the case of a blemished priest and that of an impure priest: The aspect of this case is not like the aspect of that case, and the aspect of that case is not like the aspect of this case. Their common element is that they are prohibited from performing sacrificial rites and if they performed these rites they have desecrated the service. Therefore, I will also include a non-priest, who is prohibited from performing sacrificial rites, and conclude that if he performed sacrificial rites he has desecrated the service.