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