Consider the following premises. If Michael were a sailor, then Jennifer is playing a game. If it is not late, then Michael is a sailor. It is cloudy if and only if it is late. It is not cloudy. If Jennifer plays a game, then Mary is a janitor. Can we infer the following from them? If we can, name the inference rule being used: Mary is a janitor.
 From the fact that it is cloudy if and only if it is late, and that it is not cloudy we can infer that it is not late via biconditional elimination. From the fact that if Michael were a sailor, then Jennifer is playing a game, and that if Jennifer plays a game, then Mary is a janitor we can infer that if Michael were a sailor, then Mary is a janitor via transitivity. From the fact that if it is not late, then Michael is a sailor, and that if Michael were a sailor, then Mary is a janitor we can infer that if it is not late, then Mary is a janitor via transitivity. Finally, from the fact that if it is not late, then Mary is a janitor, and that it is not late we can infer that Mary is a janitor via modus ponens. Therefore, the answer is yes.