Consider the following premises. For all x_5, if x_5 sleeps, then x_5 is poor. For all x_5, if x_5 were poor, then x_5 is a doctor. For all x_5, x_5 is an astronaut. For all x_5, if x_5 were an astronaut, then x_5 is sleeping. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is a doctor.
 From the fact that for all x_5, if x_5 sleeps, then x_5 is poor, and that for all x_5, if x_5 were poor, then x_5 is a doctor we can infer that for all x_5, if x_5 sleeps, then x_5 is a doctor via universal transitivity. From the fact that for all x_5, if x_5 were an astronaut, then x_5 is sleeping, and that for all x_5, x_5 is an astronaut we can infer that for all x_5, x_5 will sleep via universal modus ponens. Finally, from the fact that for all x_5, if x_5 sleeps, then x_5 is a doctor, and that for all x_5, x_5 will sleep we can infer that for all x_5, x_5 is a doctor via universal modus ponens. Therefore, the answer is yes.