Consider the following premises. James is not playing a game. For all x_7, x_7 is fast if and only if x_7 will play tennis. Michael is an electrician if and only if James is playing a game. Michael is an electrician if and only if Mary is fast. Can we infer the following from them? If we can, name the inference rule being used: Mary is playing tennis.
 From the fact that Michael is an electrician if and only if James is playing a game, and that James is not playing a game we can infer that Michael is not an electrician via biconditional elimination. From the fact that for all x_7, x_7 is fast if and only if x_7 will play tennis we can infer that Mary is fast if and only if Mary is playing tennis via universal instantiation. From the fact that Michael is an electrician if and only if Mary is fast, and that Michael is not an electrician we can infer that Mary is not fast via biconditional elimination. Finally, from the fact that Mary is fast if and only if Mary is playing tennis, and that Mary is not fast we can infer that Mary is not playing tennis via biconditional elimination, which contradicts that Mary is playing tennis. Therefore, the answer is no.