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