Consider the following premises. If Michael were a taxi driver, then Elisabeth is poor. For all x_12, if x_12 were poor, then x_12 is playing a game. If Elisabeth plays a game, then Michael is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: If Michael were a taxi driver, then Elisabeth is playing a game.
 From the fact that for all x_12, if x_12 were poor, then x_12 is playing a game we can infer that if Elisabeth were poor, then Elisabeth is playing a game via universal instantiation. Finally, from the fact that if Michael were a taxi driver, then Elisabeth is poor, and that if Elisabeth were poor, then Elisabeth is playing a game we can infer that if Michael were a taxi driver, then Elisabeth is playing a game via transitivity. Therefore, the answer is yes.