Consider the following premises. For all y, if y were poor, then y is reading a book. For all y, if y reads a book, then y is rich. There is at least one y for which y is poor if and only if y is rich. Can we infer the following from them? For all y, if is not true that y is rich if and only if y is poor.
 From the fact that for all y, if y were poor, then y is reading a book, and that for all y, if y reads a book, then y is rich we can infer that for all y, if y were poor, then y is rich. From the fact that there is at least one y for which y is poor if and only if y is rich we can infer that there is at least one y for which if y were rich, then y is poor. Finally, from the fact that there is at least one y for which if y were rich, then y is poor, and that for all y, if y were poor, then y is rich we can infer that there is at least one y for which y is rich if and only if y is poor, which contradicts that For all y, if is not true that y is rich if and only if y is poor. Therefore, the answer is no.