Consider the following premises. For all y, if y were a cashier, then y is playing tennis. For all y, y will not go running. For all y, if y were a cashier, then y is running. There is at least one y for which if y plays tennis, then y is a cashier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y will not play tennis.
 From the fact that for all y, if y were a cashier, then y is running, and that for all y, y will not go running we can infer that for all y, y is not a cashier via universal modus tollens. From the fact that there is at least one y for which if y plays tennis, then y is a cashier, and that for all y, if y were a cashier, then y is playing tennis we can infer that there is at least one y for which y will play tennis if and only if y is a cashier via existential biconditional introduction. Finally, from the fact that there is at least one y for which y will play tennis if and only if y is a cashier, and that for all y, y is not a cashier we can infer that there is at least one y for which y will not play tennis via existential biconditional elimination. Therefore, the answer is yes.