Consider the following premises. For all x_1, x_1 will play tennis or x_1 will not work. For all x_1, x_1 will play a game if and only if x_1 will work. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, if x_1 plays a game, then x_1 is playing tennis.
 From the fact that for all x_1, x_1 will play tennis or x_1 will not work we can infer that for all x_1, if x_1 works, then x_1 is playing tennis via universal rewriting. From the fact that for all x_1, x_1 will play a game if and only if x_1 will work we can infer that for all x_1, if x_1 plays a game, then x_1 is working via universal biconditional elimination. Finally, from the fact that for all x_1, if x_1 plays a game, then x_1 is working, and that for all x_1, if x_1 works, then x_1 is playing tennis we can infer that for all x_1, if x_1 plays a game, then x_1 is playing tennis via universal transitivity. Therefore, the answer is yes.