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