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