Consider the following premises. There is at least one x_7 for which if x_7 were bored, then x_7 is playing tennis. For all x_7, x_7 will not play a game. For all x_7, x_7 will play a game if and only if x_7 is poor. For all x_7, x_7 is poor if and only if x_7 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 is not bored.
 From the fact that for all x_7, x_7 will play a game if and only if x_7 is poor, and that for all x_7, x_7 will not play a game we can infer that for all x_7, x_7 is not poor via universal biconditional elimination. From the fact that for all x_7, x_7 is poor if and only if x_7 will play tennis, and that for all x_7, x_7 is not poor we can infer that for all x_7, x_7 will not play tennis via universal biconditional elimination. Finally, from the fact that there is at least one x_7 for which if x_7 were bored, then x_7 is playing tennis, and that for all x_7, x_7 will not play tennis we can infer that there is at least one x_7 for which x_7 is not bored via existential modus tollens. Therefore, the answer is yes.