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