Consider the following premises. For all y, if y were a soldier, then y is sleeping. For all y, y will sleep or y is not a soldier. There is at least one y for which if y sleeps, then y is a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all y, if is not true that y will sleep if and only if y is a soldier.
 From the fact that there is at least one y for which if y sleeps, then y is a soldier, and that for all y, if y were a soldier, then y is sleeping we can infer that there is at least one y for which y will sleep if and only if y is a soldier via existential biconditional introduction. From the fact that there is at least one y for which y will sleep if and only if y is a soldier we can infer that there is at least one y for which if y sleeps, then y is a soldier via existential biconditional elimination. From the fact that for all y, y will sleep or y is not a soldier we can infer that for all y, if y were a soldier, then y is sleeping via universal rewriting. Finally, from the fact that there is at least one y for which if y sleeps, then y is a soldier, and that for all y, if y were a soldier, then y is sleeping we can infer that there is at least one y for which y will sleep if and only if y is a soldier via existential biconditional introduction, which contradicts that For all y, if is not true that y will sleep if and only if y is a soldier. Therefore, the answer is no.