Consider the following premises. For all y, y is rich or y is not a cashier. There is at least one y for which if y drives a car, then y is a cashier. For all y, if y were rich, then y is driving a car. Can we infer the following from them? There is at least one y for which y is rich if and only if y is a cashier.
 From the fact that for all y, y is rich or y is not a cashier we can infer that for all y, if y were a cashier, then y is rich. From the fact that for all y, if y were rich, then y is driving a car, and that there is at least one y for which if y drives a car, then y is a cashier we can infer that there is at least one y for which if y were rich, then y is a cashier. Finally, from the fact that there is at least one y for which if y were rich, then y is a cashier, and that for all y, if y were a cashier, then y is rich we can infer that there is at least one y for which y is rich if and only if y is a cashier. Therefore, the answer is yes.