Consider the following premises. For all y, y is fast if and only if y will cook. For all y, if y plays squash, then y is fast. For all y, if y cooks, then y is playing squash. For all y, y will not play squash. 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 cook.
 From the fact that for all y, y is fast if and only if y will cook we can infer that for all y, if y were fast, then y is cooking via universal biconditional elimination. From the fact that for all y, if y plays squash, then y is fast, and that for all y, if y were fast, then y is cooking we can infer that for all y, if y plays squash, then y is cooking via universal transitivity. From the fact that for all y, if y cooks, then y is playing squash, and that for all y, if y plays squash, then y is cooking we can infer that for all y, y will cook if and only if y will play squash via universal biconditional introduction. Finally, from the fact that for all y, y will cook 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 will not cook via universal biconditional elimination, which contradicts that There is at least one y for which y will cook. Therefore, the answer is no.