Consider the following premises. Richard is not playing tennis. For all x_2, x_2 is a mechanic if and only if x_2 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: Richard is not a mechanic.
 From the fact that for all x_2, x_2 is a mechanic if and only if x_2 will play tennis we can infer that Richard is a mechanic if and only if Richard is playing tennis via universal instantiation. Finally, from the fact that Richard is a mechanic if and only if Richard is playing tennis, and that Richard is not playing tennis we can infer that Richard is not a mechanic via biconditional elimination. Therefore, the answer is yes.