Consider the following premises. For all y, if y climbs a mountain, then y is a scientist. There is at least one y for which if y were a scientist, then y is climbing a mountain. For all y, if y were a scientist, then y is climbing a mountain. Can we infer the following from them? For all y, if is not true that y will climb a mountain if and only if y is a scientist.
 From the fact that there is at least one y for which if y were a scientist, then y is climbing a mountain, and that for all y, if y climbs a mountain, then y is a scientist we can infer that there is at least one y for which y is a scientist if and only if y will climb a mountain. From the fact that there is at least one y for which y is a scientist if and only if y will climb a mountain we can infer that there is at least one y for which if y climbs a mountain, then y is a scientist. Finally, from the fact that there is at least one y for which if y climbs a mountain, then y is a scientist, and that for all y, if y were a scientist, 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 scientist, which contradicts that For all y, if is not true that y will climb a mountain if and only if y is a scientist. Therefore, the answer is no.