Consider the following premises. For all y_3, if y_3 were a nurse, then y_3 is a mechanic. For all y_3, y_3 is not a nurse. For all y_3, y_3 is a nurse if and only if y_3 is a mechanic. Can we infer the following from them? There is at least one y_3 for which y_3 is a mechanic.
 From the fact that for all y_3, y_3 is a nurse if and only if y_3 is a mechanic we can infer that for all y_3, if y_3 were a mechanic, then y_3 is a nurse. From the fact that for all y_3, if y_3 were a mechanic, then y_3 is a nurse, and that for all y_3, if y_3 were a nurse, then y_3 is a mechanic we can infer that for all y_3, y_3 is a mechanic if and only if y_3 is a nurse. Finally, from the fact that for all y_3, y_3 is a mechanic if and only if y_3 is a nurse, and that for all y_3, y_3 is not a nurse we can infer that for all y_3, y_3 is not a mechanic, which contradicts that There is at least one y_3 for which y_3 is a mechanic. Therefore, the answer is no.