Can a conditional statement have multiple premises? Is it correct to say that a conditional statement of the form p ^ q -> r has multiple premises (where the premises are the individual conjuncts p and q) or is that an incorrect use of the term "premise" when referring to implications (as the conjunction itself could be considered the only "premise" of the implication)? I ask because, in Rosen's Discrete Mathematics and its Applications, he claims that "A theorem may be the universal quantification of a conditional statement with one or more premises and a conclusion". I am unsure whether he is referencing the premises and conclusion of the universally quantified conditional statement or the premises and conclusion of something else, such as the premises assumed to be true so that the theorem can be concluded.

To prove a mathematical theorem you assume your premise and do your best to get to the conclusion. Very often, the premise you are assuming that's true contains a lot of claims. If you let each of those claims be a logical letter such as p,q, and so on, you'll get the structure that you're asking, a "multiple premises".
