Consider the following premises. For all z, z is a police officer if and only if z is curious. There is at least one z for which if z plays a game, then z is curious. 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 a game, then z is a police officer.
 From the fact that for all z, z is a police officer if and only if z is curious we can infer that for all z, if z were curious, then z is a police officer via universal biconditional elimination. Finally, from the fact that there is at least one z for which if z plays a game, then z is curious, and that for all z, if z were curious, then z is a police officer we can infer that there is at least one z for which if z plays a game, then z is a police officer via existential transitivity. Therefore, the answer is yes.