Consider the following premises. For all y, y is not a nurse. For all y, if y were a nurse, then y is playing squash. For all y, if y plays squash, then y is a nurse. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which y will play squash.
 From the fact that for all y, if y plays squash, then y is a nurse, and that for all y, if y were a nurse, then y is playing squash we can infer that for all y, y will play squash if and only if y is a nurse via universal biconditional introduction. Finally, from the fact that for all y, y will play squash if and only if y is a nurse, and that for all y, y is not a nurse we can infer that for all y, y will not play squash via universal biconditional elimination, which contradicts that There is at least one y for which y will play squash. Therefore, the answer is no.