Consider the following premises. Charles is a janitor or Barbara is not playing tennis. Barbara is playing tennis if and only if Charles is a janitor. If Barbara plays tennis, then Charles is a janitor. Can we infer the following from them? If we can, name the inference rule being used: Charles is a janitor if and only if Barbara is playing tennis.
 From the fact that Charles is a janitor or Barbara is not playing tennis we can infer that if Barbara plays tennis, then Charles is a janitor via rewriting. From the fact that Barbara is playing tennis if and only if Charles is a janitor we can infer that if Charles were a janitor, then Barbara is playing tennis via biconditional elimination. From the fact that if Barbara plays tennis, then Charles is a janitor, and that if Charles were a janitor, then Barbara is playing tennis we can infer that Barbara is playing tennis if and only if Charles is a janitor via biconditional introduction. From the fact that Barbara is playing tennis if and only if Charles is a janitor we can infer that if Charles were a janitor, then Barbara is playing tennis via biconditional elimination. Finally, from the fact that if Charles were a janitor, then Barbara is playing tennis, and that if Barbara plays tennis, then Charles is a janitor we can infer that Charles is a janitor if and only if Barbara is playing tennis via biconditional introduction. Therefore, the answer is yes.