Consider the following premises. There is at least one z for which z is a politician if and only if z will play squash. For all z, z will play a game or z is not a politician. 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 plays squash, then z is playing a game.
 From the fact that for all z, z will play a game or z is not a politician we can infer that for all z, if z were a politician, then z is playing a game via universal rewriting. From the fact that there is at least one z for which z is a politician 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 politician 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 politician, and that for all z, if z were a politician, then z is playing a game we can infer that there is at least one z for which if z plays squash, then z is playing a game via existential transitivity. Therefore, the answer is yes.