Consider the following premises. There is at least one x_6 for which if x_6 plays tennis, then x_6 is a taxi driver. For all x_6, if x_6 were a taxi driver, then x_6 is playing tennis. For all x_6, x_6 will not play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is not a taxi driver.
 From the fact that there is at least one x_6 for which if x_6 plays tennis, then x_6 is a taxi driver, and that for all x_6, if x_6 were a taxi driver, then x_6 is playing tennis we can infer that there is at least one x_6 for which x_6 will play tennis if and only if x_6 is a taxi driver via existential biconditional introduction. From the fact that there is at least one x_6 for which x_6 will play tennis if and only if x_6 is a taxi driver we can infer that there is at least one x_6 for which if x_6 were a taxi driver, then x_6 is playing tennis via existential biconditional elimination. Finally, from the fact that there is at least one x_6 for which if x_6 were a taxi driver, then x_6 is playing tennis, and that for all x_6, x_6 will not play tennis we can infer that there is at least one x_6 for which x_6 is not a taxi driver via existential modus tollens. Therefore, the answer is yes.