Consider the following premises. For all x_5, if x_5 cooks, then x_5 is fast. For all x_5, if x_5 writes a letter, then x_5 is driving a car. For all x_5, if x_5 were fast, then x_5 is writing a letter. For all x_5, x_5 will cook. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will drive a car.
 From the fact that for all x_5, if x_5 cooks, then x_5 is fast, and that for all x_5, if x_5 were fast, then x_5 is writing a letter we can infer that for all x_5, if x_5 cooks, then x_5 is writing a letter via universal transitivity. From the fact that for all x_5, if x_5 cooks, then x_5 is writing a letter, and that for all x_5, if x_5 writes a letter, then x_5 is driving a car we can infer that for all x_5, if x_5 cooks, then x_5 is driving a car via universal transitivity. Finally, from the fact that for all x_5, if x_5 cooks, then x_5 is driving a car, and that for all x_5, x_5 will cook we can infer that for all x_5, x_5 will drive a car via universal modus ponens. Therefore, the answer is yes.