Consider the following premises. For all y_3, y_3 will not sleep. There is at least one y_3 for which y_3 will sleep if and only if y_3 will play squash. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_3 for which y_3 will not play squash.
 From the fact that there is at least one y_3 for which y_3 will sleep if and only if y_3 will play squash we can infer that there is at least one y_3 for which if y_3 plays squash, then y_3 is sleeping via existential biconditional elimination. Finally, from the fact that there is at least one y_3 for which if y_3 plays squash, then y_3 is sleeping, and that for all y_3, y_3 will not sleep we can infer that there is at least one y_3 for which y_3 will not play squash via existential modus tollens. Therefore, the answer is yes.