Consider the following premises. For all x_1, if x_1 works, then x_1 is sleeping. For all x_1, if x_1 were fast, then x_1 is a police officer. For all x_1, if x_1 sleeps, then x_1 is fast. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, if x_1 works, then x_1 is a police officer.
 From the fact that for all x_1, if x_1 works, then x_1 is sleeping, and that for all x_1, if x_1 sleeps, then x_1 is fast we can infer that for all x_1, if x_1 works, then x_1 is fast via universal transitivity. Finally, from the fact that for all x_1, if x_1 works, then x_1 is fast, and that for all x_1, if x_1 were fast, then x_1 is a police officer we can infer that for all x_1, if x_1 works, then x_1 is a police officer via universal transitivity. Therefore, the answer is yes.