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