Consider the following premises. For all y, y will read a book if and only if y is a nurse. There is at least one y for which if y reads a book, then y is a nurse. Can we infer the following from them? There is at least one y for which if y were a nurse, then y is reading a book.
 From the fact that for all y, y will read a book if and only if y is a nurse we can infer that for all y, if y were a nurse, then y is reading a book. From the fact that for all y, if y were a nurse, then y is reading a book, and that there is at least one y for which if y reads a book, then y is a nurse we can infer that there is at least one y for which y is a nurse if and only if y will read a book. Finally, from the fact that there is at least one y for which y is a nurse if and only if y will read a book we can infer that there is at least one y for which if y were a nurse, then y is reading a book. Therefore, the answer is yes.