Related על פסחים 5:2

One who slaughtered [the Passover offering] for its purpose but completed [the rituals associated with the sacrifice] for a different purpose -- it is valid because [a sacrifice] is rendered valid through the slaughter. How is it "slaughtered for those who cannot eat it" (Pes. 5:3)? [This applies where] he slaughtered for a sick person or for an elderly person who cannot eat an olive's-bulk. How is it [slaughtered] for "those who are not registered" (ibid.)? [This applies where] he slaughtered it for members of a different collective. [If] he slaughtered for [both] circumcised and uncircumcised, or for [both] impure persons and for pure persons, it is valid. Abba Shaul disqualifies it, and it is logical that it should be disqualified, since [a person's unfit status] at the time [of the sacrifice] disqualifies [a sacrifice], and an uncircumcised person is disqualified *and an impure person is disqualified (following the GR"A). Just as "the time" (i.e., where the butcher both intends that sacrifice be eaten in its proper time and not at its proper time, see Minchat Bikkurim) makes it [disqualified under the principle of] "the part is like the whole," so too an uncircumcised person makes it [disqualified under] "the part is like the whole." Or perhaps look at it this way: Since an impure person and an uncircumcised person are disqualified, just as [partial] impurity does not cause [application of the principle] "the part is like the whole," thus so too a [partially] uncircumcised person does not cause [application of the principle] "the part is like the whole." Let us see to what case it is similar: We derive a matter that does not apply to every offering (i.e., lack of circumcision), from a [different] matter that does not apply to every offering (i.e., impurity), and it is proven from "time," which [also] does not apply to all offerings. Or perhaps look at it this way: We derive a matter which does not permit exception to a general prohibition, from a [different] matter which does not permit an exception to a general prohibition, and it is not proven from impurity, which does permit an exception to a general prohibition.