 If the first premise didn’t have this form, the inference wouldn’t be an instance of ‘B if A, and A; so B’. It isn’t obvious that all impeccable inferences are instances of a more general valid form, much less inferences whose impeccability is due to the forms of the relevant propositions. But this thought has served as an ideal for the study of valid inference, at least since Aristotle’s treatment of examples like (2).