Consider the following premises. For all y_3, if y_3 were a nurse, then y_3 is rich. For all y_3, y_3 is not rich. For all y_3, if y_3 were rich, then y_3 is a nurse. Can we infer the following from them? For all y_3, y_3 is not a nurse.
 From the fact that for all y_3, if y_3 were rich, then y_3 is a nurse, and that for all y_3, if y_3 were a nurse, then y_3 is rich we can infer that for all y_3, y_3 is rich if and only if y_3 is a nurse. From the fact that for all y_3, y_3 is rich if and only if y_3 is a nurse we can infer that for all y_3, if y_3 were a nurse, then y_3 is rich. Finally, from the fact that for all y_3, if y_3 were a nurse, then y_3 is rich, and that for all y_3, y_3 is not rich we can infer that for all y_3, y_3 is not a nurse. Therefore, the answer is yes.