Consider the following premises. For all x, if x plays squash, then x is a politician. For all x, if x were an artist, then x is playing squash. There is at least one x for which if x were a politician, then x is an artist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which if x were an artist, then x is playing squash.
 From the fact that for all x, if x plays squash, then x is a politician, and that there is at least one x for which if x were a politician, then x is an artist we can infer that there is at least one x for which if x plays squash, then x is an artist via existential transitivity. From the fact that there is at least one x for which if x plays squash, then x is an artist, and that for all x, if x were an artist, then x is playing squash we can infer that there is at least one x for which x will play squash if and only if x is an artist via existential biconditional introduction. Finally, from the fact that there is at least one x for which x will play squash if and only if x is an artist we can infer that there is at least one x for which if x were an artist, then x is playing squash via existential biconditional elimination. Therefore, the answer is yes.