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