Consider the following premises. There is at least one x_4 for which if x_4 plays a game, then x_4 is curious. For all x_4, if x_4 were curious, then x_4 is an electrician. For all x_4, if x_4 were curious, then x_4 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which if x_4 plays a game, then x_4 is an electrician.
 From the fact that for all x_4, if x_4 were curious, then x_4 is playing a game, and that there is at least one x_4 for which if x_4 plays a game, then x_4 is curious we can infer that there is at least one x_4 for which x_4 is curious if and only if x_4 will play a game via existential biconditional introduction. From the fact that there is at least one x_4 for which x_4 is curious if and only if x_4 will play a game we can infer that there is at least one x_4 for which if x_4 plays a game, then x_4 is curious via existential biconditional elimination. Finally, from the fact that there is at least one x_4 for which if x_4 plays a game, then x_4 is curious, and that for all x_4, if x_4 were curious, then x_4 is an electrician we can infer that there is at least one x_4 for which if x_4 plays a game, then x_4 is an electrician via existential transitivity. Therefore, the answer is yes.