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