Consider the following premises. For all x_2, if x_2 plays tennis, then x_2 is a taxi driver. For all x_2, if x_2 were a taxi driver, then x_2 is playing tennis. For all x_2, x_2 will sleep. For all x_2, if x_2 plays tennis, then x_2 is not sleeping. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 is not a taxi driver.
 From the fact that for all x_2, if x_2 were a taxi driver, then x_2 is playing tennis, and that for all x_2, if x_2 plays tennis, then x_2 is a taxi driver we can infer that for all x_2, x_2 is a taxi driver if and only if x_2 will play tennis via universal biconditional introduction. From the fact that for all x_2, if x_2 plays tennis, then x_2 is not sleeping, and that for all x_2, x_2 will sleep we can infer that for all x_2, x_2 will not play tennis via universal modus tollens. Finally, from the fact that for all x_2, x_2 is a taxi driver if and only if x_2 will play tennis, and that for all x_2, x_2 will not play tennis we can infer that for all x_2, x_2 is not a taxi driver via universal biconditional elimination. Therefore, the answer is yes.