Consider the following premises. For all x_15, if x_15 plays a game, then x_15 is a sailor. For all x_15, x_15 will play a game if and only if x_15 will drive a car. There is at least one x_15 for which x_15 will drive a car if and only if x_15 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_15 for which if x_15 drives a car, then x_15 is a sailor.
 From the fact that for all x_15, x_15 will play a game if and only if x_15 will drive a car we can infer that for all x_15, if x_15 drives a car, then x_15 is playing a game via universal biconditional elimination. From the fact that for all x_15, if x_15 drives a car, then x_15 is playing a game, and that for all x_15, if x_15 plays a game, then x_15 is a sailor we can infer that for all x_15, if x_15 drives a car, then x_15 is a sailor via universal transitivity. From the fact that there is at least one x_15 for which x_15 will drive a car if and only if x_15 is a sailor we can infer that there is at least one x_15 for which if x_15 were a sailor, then x_15 is driving a car via existential biconditional elimination. From the fact that for all x_15, if x_15 drives a car, then x_15 is a sailor, and that there is at least one x_15 for which if x_15 were a sailor, then x_15 is driving a car we can infer that there is at least one x_15 for which x_15 will drive a car if and only if x_15 is a sailor via existential biconditional introduction. Finally, from the fact that there is at least one x_15 for which x_15 will drive a car if and only if x_15 is a sailor we can infer that there is at least one x_15 for which if x_15 drives a car, then x_15 is a sailor via existential biconditional elimination. Therefore, the answer is yes.