Consider the following premises. For all x_4, if x_4 sleeps, then x_4 is playing a game. For all x_4, x_4 will sleep or x_4 is not a doctor. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, if x_4 were a doctor, then x_4 is playing a game.
 From the fact that for all x_4, x_4 will sleep or x_4 is not a doctor we can infer that for all x_4, if x_4 were a doctor, then x_4 is sleeping via universal rewriting. Finally, from the fact that for all x_4, if x_4 were a doctor, then x_4 is sleeping, and that for all x_4, if x_4 sleeps, then x_4 is playing a game we can infer that for all x_4, if x_4 were a doctor, then x_4 is playing a game via universal transitivity. Therefore, the answer is yes.