Consider the following premises. For all x, if x were a soldier, then x is rich. For all x, if x were rich, then x is a soldier. For all x, if x were a soldier, then x is rich. For all x, x is not rich. Can we infer the following from them? For all x, x is not a soldier.
 From the fact that for all x, if x were rich, then x is a soldier, and that for all x, if x were a soldier, then x is rich we can infer that for all x, x is rich if and only if x is a soldier. From the fact that for all x, x is rich if and only if x is a soldier we can infer that for all x, if x were rich, then x is a soldier. From the fact that for all x, if x were a soldier, then x is rich, and that for all x, if x were rich, then x is a soldier we can infer that for all x, x is a soldier if and only if x is rich. Finally, from the fact that for all x, x is a soldier if and only if x is rich, and that for all x, x is not rich we can infer that for all x, x is not a soldier. Therefore, the answer is yes.