Consider the following premises. For all x_9, if x_9 plays a game, then x_9 is driving a car. For all x_9, if x_9 plays tennis, then x_9 is a poet. For all x_9, if x_9 were a poet, then x_9 is playing a game. For all x_9, x_9 will play tennis if and only if x_9 will drive a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 will play tennis if and only if x_9 is a poet.
 From the fact that for all x_9, if x_9 were a poet, then x_9 is playing a game, and that for all x_9, if x_9 plays a game, then x_9 is driving a car we can infer that for all x_9, if x_9 were a poet, then x_9 is driving a car via universal transitivity. From the fact that for all x_9, x_9 will play tennis if and only if x_9 will drive a car we can infer that for all x_9, if x_9 drives a car, then x_9 is playing tennis via universal biconditional elimination. From the fact that for all x_9, if x_9 were a poet, then x_9 is driving a car, and that for all x_9, if x_9 drives a car, then x_9 is playing tennis we can infer that for all x_9, if x_9 were a poet, then x_9 is playing tennis via universal transitivity. Finally, from the fact that for all x_9, if x_9 plays tennis, then x_9 is a poet, and that for all x_9, if x_9 were a poet, then x_9 is playing tennis we can infer that for all x_9, x_9 will play tennis if and only if x_9 is a poet via universal biconditional introduction. Therefore, the answer is yes.