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