(Ibid. 12:15) "the unclean one may eat of it": This tells me only that the unclean one may eat of it (of disqualified offerings that have been redeemed). Whence do I derive that the clean one (may eat of it)? From "the unclean one and the clean one may eat of it": Scripture hereby apprises us that they both may eat of it from the same dish.
I might think that terumah (that has become tamei) may also be eaten from the same dish; it is, therefore, written shall eat it" — This (disqualified offerings that have been redeemed) from the same dish, but not terumah.