Consider the following premises. For all y, if y climbs a mountain, then y is reading a book. For all y, if y climbs a mountain, then y is a soldier. For all y, y will not read a book. There is at least one y for which if y were a soldier, then y is climbing a mountain. 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 is not a soldier.
 From the fact that for all y, if y climbs a mountain, then y is reading a book, and that for all y, y will not read a book we can infer that for all y, y will not climb a mountain via universal modus tollens. From the fact that for all y, if y climbs a mountain, then y is a soldier, and that there is at least one y for which if y were a soldier, then y is climbing a mountain we can infer that there is at least one y for which y will climb a mountain if and only if y is a soldier via existential biconditional introduction. Finally, from the fact that there is at least one y for which y will climb a mountain if and only if y is a soldier, and that for all y, y will not climb a mountain we can infer that there is at least one y for which y is not a soldier via existential biconditional elimination. Therefore, the answer is yes.