Consider the following premises. For all y_1, y_1 will sleep or y_1 is not a mechanic. There is at least one y_1 for which if y_1 sleeps, then y_1 is a mechanic. Can we infer the following from them? There is at least one y_1 for which if y_1 were a mechanic, then y_1 is sleeping.
 From the fact that for all y_1, y_1 will sleep or y_1 is not a mechanic we can infer that for all y_1, if y_1 were a mechanic, then y_1 is sleeping. From the fact that there is at least one y_1 for which if y_1 sleeps, then y_1 is a mechanic, and that for all y_1, if y_1 were a mechanic, then y_1 is sleeping we can infer that there is at least one y_1 for which y_1 will sleep if and only if y_1 is a mechanic. Finally, from the fact that there is at least one y_1 for which y_1 will sleep if and only if y_1 is a mechanic we can infer that there is at least one y_1 for which if y_1 were a mechanic, then y_1 is sleeping. Therefore, the answer is yes.