Consider the following premises. There is at least one x_3 for which if x_3 plays tennis, then x_3 is a police officer. For all x_3, if x_3 were a police officer, then x_3 is cooking. For all x_3, if x_3 cooks, then x_3 is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which if x_3 were a police officer, then x_3 is playing tennis.
 From the fact that for all x_3, if x_3 were a police officer, then x_3 is cooking, and that for all x_3, if x_3 cooks, then x_3 is playing tennis we can infer that for all x_3, if x_3 were a police officer, then x_3 is playing tennis via universal transitivity. From the fact that for all x_3, if x_3 were a police officer, then x_3 is playing tennis, and that there is at least one x_3 for which if x_3 plays tennis, then x_3 is a police officer we can infer that there is at least one x_3 for which x_3 is a police officer if and only if x_3 will play tennis via existential biconditional introduction. Finally, from the fact that there is at least one x_3 for which x_3 is a police officer if and only if x_3 will play tennis we can infer that there is at least one x_3 for which if x_3 were a police officer, then x_3 is playing tennis via existential biconditional elimination. Therefore, the answer is yes.