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