Consider the following premises. For all y, y is excited if and only if y will play squash. For all y, y will not play squash. For all y, if y were excited, then y is happy. For all y, if y were happy, then y is excited. Can we infer the following from them? For all y, y is not happy.
 From the fact that for all y, if y were happy, then y is excited, and that for all y, if y were excited, then y is happy we can infer that for all y, y is happy if and only if y is excited. From the fact that for all y, y is excited if and only if y will play squash, and that for all y, y will not play squash we can infer that for all y, y is not excited. Finally, from the fact that for all y, y is happy if and only if y is excited, and that for all y, y is not excited we can infer that for all y, y is not happy. Therefore, the answer is yes.