Consider the following premises. For all y, y is not excited. For all y, if y were an astronaut, then y is a soldier. For all y, if y climbs a mountain, then y is an astronaut. For all y, y is a soldier if and only if y is excited. Can we infer the following from them? If we can, name the inference rule being used: For all y, y will not climb a mountain.
 From the fact that for all y, y is a soldier if and only if y is excited, and that for all y, y is not excited we can infer that for all y, y is not a soldier via universal biconditional elimination. From the fact that for all y, if y were an astronaut, then y is a soldier, and that for all y, y is not a soldier we can infer that for all y, y is not an astronaut via universal modus tollens. Finally, from the fact that for all y, if y climbs a mountain, then y is an astronaut, and that for all y, y is not an astronaut we can infer that for all y, y will not climb a mountain via universal modus tollens. Therefore, the answer is yes.