Consider the following premises. For all y_3, y_3 will play tennis if and only if y_3 is a janitor. David is not a janitor. Can we infer the following from them? If we can, name the inference rule being used: David is not playing tennis.
 From the fact that for all y_3, y_3 will play tennis if and only if y_3 is a janitor we can infer that David is playing tennis if and only if David is a janitor via universal instantiation. From the fact that David is playing tennis if and only if David is a janitor we can infer that if David plays tennis, then David is a janitor via biconditional elimination. Finally, from the fact that if David plays tennis, then David is a janitor, and that David is not a janitor we can infer that David is not playing tennis via modus tollens. Therefore, the answer is yes.