Consider the following premises. There is at least one y for which y will play tennis if and only if y is a lawyer. For all y, if y plays tennis, then y is excited. For all y, if y were excited, then y is playing tennis. For all y, y is not excited. Can we infer the following from them? If we can, name the inference rule being used: For all y, y is a lawyer.
 From the fact that for all y, if y were excited, then y is playing tennis, and that for all y, if y plays tennis, then y is excited we can infer that for all y, y is excited if and only if y will play tennis via universal biconditional introduction. From the fact that for all y, y is excited if and only if y will play tennis, and that for all y, y is not excited we can infer that for all y, y will not play tennis via universal biconditional elimination. Finally, from the fact that there is at least one y for which y will play tennis if and only if y is a lawyer, and that for all y, y will not play tennis we can infer that there is at least one y for which y is not a lawyer via existential biconditional elimination, which contradicts that For all y, y is a lawyer. Therefore, the answer is no.