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