Consider the following premises. For all x_7, x_7 will work if and only if x_7 is a mechanic. For all x_7, if x_7 drives a car, then x_7 is a soldier. For all x_7, if x_7 were a soldier, then x_7 is working. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, if x_7 drives a car, then x_7 is a mechanic.
 From the fact that for all x_7, x_7 will work if and only if x_7 is a mechanic we can infer that for all x_7, if x_7 works, then x_7 is a mechanic via universal biconditional elimination. From the fact that for all x_7, if x_7 were a soldier, then x_7 is working, and that for all x_7, if x_7 works, then x_7 is a mechanic we can infer that for all x_7, if x_7 were a soldier, then x_7 is a mechanic via universal transitivity. Finally, from the fact that for all x_7, if x_7 drives a car, then x_7 is a soldier, and that for all x_7, if x_7 were a soldier, then x_7 is a mechanic we can infer that for all x_7, if x_7 drives a car, then x_7 is a mechanic via universal transitivity. Therefore, the answer is yes.