Consider the following premises. For all x_8, if x_8 plays a game, then x_8 is playing tennis. For all x_8, if x_8 plays a game, then x_8 is playing tennis. For all x_8, if x_8 plays tennis, then x_8 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: If Richard plays a game, then Richard is playing tennis.
 From the fact that for all x_8, if x_8 plays tennis, then x_8 is playing a game, and that for all x_8, if x_8 plays a game, then x_8 is playing tennis we can infer that for all x_8, x_8 will play tennis if and only if x_8 will play a game via universal biconditional introduction. From the fact that for all x_8, x_8 will play tennis if and only if x_8 will play a game we can infer that for all x_8, if x_8 plays tennis, then x_8 is playing a game via universal biconditional elimination. From the fact that for all x_8, if x_8 plays a game, then x_8 is playing tennis, and that for all x_8, if x_8 plays tennis, then x_8 is playing a game we can infer that for all x_8, x_8 will play a game if and only if x_8 will play tennis via universal biconditional introduction. From the fact that for all x_8, x_8 will play a game if and only if x_8 will play tennis we can infer that Richard is playing a game if and only if Richard is playing tennis via universal instantiation. Finally, from the fact that Richard is playing a game if and only if Richard is playing tennis we can infer that if Richard plays a game, then Richard is playing tennis via biconditional elimination. Therefore, the answer is yes.