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