Consider the following premises. There is at least one z for which if z were rich, then z is playing tennis. For all z, if z were a sailor, then z is rich. For all z, z is a sailor if and only if z will 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 z will play tennis if and only if z is a sailor.
 From the fact that for all z, z is a sailor if and only if z will play tennis we can infer that for all z, if z plays tennis, then z is a sailor via universal biconditional elimination. From the fact that for all z, if z were a sailor, then z is rich, and that there is at least one z for which if z were rich, then z is playing tennis we can infer that there is at least one z for which if z were a sailor, then z is playing tennis via existential transitivity. Finally, from the fact that for all z, if z plays tennis, then z is a sailor, and that there is at least one z for which if z were a sailor, then z is playing tennis we can infer that there is at least one z for which z will play tennis if and only if z is a sailor via existential biconditional introduction. Therefore, the answer is yes.