Consider the following premises. There is at least one z for which z will work if and only if z will play tennis. For all z, z is excited or z will not play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which if z works, then z is excited.
 From the fact that there is at least one z for which z will work if and only if z will play tennis we can infer that there is at least one z for which if z works, then z is playing tennis via existential biconditional elimination. From the fact that for all z, z is excited or z will not play tennis we can infer that for all z, if z plays tennis, then z is excited via universal rewriting. Finally, from the fact that there is at least one z for which if z works, then z is playing tennis, and that for all z, if z plays tennis, then z is excited we can infer that there is at least one z for which if z works, then z is excited via existential transitivity. Therefore, the answer is yes.