Consider the following premises. It is not late. It is sunny if and only if James is a janitor. If it is sunny, then it is cloudy. It is cloudy if and only if it is late. Can we infer the following from them? If we can, name the inference rule being used: James is not a janitor.
 From the fact that it is sunny if and only if James is a janitor we can infer that if James were a janitor, then it is sunny via biconditional elimination. From the fact that it is cloudy if and only if it is late, and that it is not late we can infer that it is not cloudy via biconditional elimination. From the fact that if it is sunny, then it is cloudy, and that it is not cloudy we can infer that it is not sunny via modus tollens. Finally, from the fact that if James were a janitor, then it is sunny, and that it is not sunny we can infer that James is not a janitor via modus tollens. Therefore, the answer is yes.