Consider the following premises. For all x_5, if x_5 plays tennis, then x_5 is a carpenter. For all x_5, if x_5 were a carpenter, then x_5 is playing a game. For all x_5, x_5 is a politician if and only if x_5 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, if x_5 were a politician, then x_5 is playing a game.
 From the fact that for all x_5, if x_5 plays tennis, then x_5 is a carpenter, and that for all x_5, if x_5 were a carpenter, then x_5 is playing a game we can infer that for all x_5, if x_5 plays tennis, then x_5 is playing a game via universal transitivity. From the fact that for all x_5, x_5 is a politician if and only if x_5 will play tennis we can infer that for all x_5, if x_5 were a politician, then x_5 is playing tennis via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 were a politician, then x_5 is playing tennis, and that for all x_5, if x_5 plays tennis, then x_5 is playing a game we can infer that for all x_5, if x_5 were a politician, then x_5 is playing a game via universal transitivity. Therefore, the answer is yes.