Consider the following premises. For all y, y is an office clerk if and only if y is a mechanic. There is at least one y for which y is not a mechanic. For all y, if y were an office clerk, then y is a mechanic. Can we infer the following from them? There is at least one y for which y is not an office clerk.
 From the fact that for all y, y is an office clerk if and only if y is a mechanic we can infer that for all y, if y were a mechanic, then y is an office clerk. From the fact that for all y, if y were an office clerk, then y is a mechanic, and that for all y, if y were a mechanic, then y is an office clerk we can infer that for all y, y is an office clerk if and only if y is a mechanic. Finally, from the fact that for all y, y is an office clerk if and only if y is a mechanic, and that there is at least one y for which y is not a mechanic we can infer that there is at least one y for which y is not an office clerk. Therefore, the answer is yes.