Consider the following premises. For all x_5, if x_5 plays tennis, then x_5 is listening to a song. For all x_5, if x_5 listens to a song, then x_5 is a soldier. For all x_5, if x_5 writes a letter, then x_5 is an office clerk. For all x_5, if x_5 were a soldier, then x_5 is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, if x_5 plays tennis, then x_5 is an office clerk.
 From the fact that for all x_5, if x_5 plays tennis, then x_5 is listening to a song, and that for all x_5, if x_5 listens to a song, then x_5 is a soldier we can infer that for all x_5, if x_5 plays tennis, then x_5 is a soldier via universal transitivity. From the fact that for all x_5, if x_5 were a soldier, then x_5 is writing a letter, and that for all x_5, if x_5 writes a letter, then x_5 is an office clerk we can infer that for all x_5, if x_5 were a soldier, then x_5 is an office clerk via universal transitivity. Finally, from the fact that for all x_5, if x_5 plays tennis, then x_5 is a soldier, and that for all x_5, if x_5 were a soldier, then x_5 is an office clerk we can infer that for all x_5, if x_5 plays tennis, then x_5 is an office clerk via universal transitivity. Therefore, the answer is yes.