Consider the following premises. For all y, if y were a lawyer, then y is climbing a mountain. There is at least one y for which if y drinks water, then y is a lawyer. For all y, y will drink water or y will not climb a mountain. Can we infer the following from them? There is at least one y for which y will climb a mountain if and only if y is a lawyer.
 From the fact that for all y, y will drink water or y will not climb a mountain we can infer that for all y, if y climbs a mountain, then y is drinking water. From the fact that for all y, if y climbs a mountain, then y is drinking water, and that there is at least one y for which if y drinks water, then y is a lawyer we can infer that there is at least one y for which if y climbs a mountain, then y is a lawyer. Finally, from the fact that there is at least one y for which if y climbs a mountain, then y is a lawyer, and that for all y, if y were a lawyer, 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 lawyer. Therefore, the answer is yes.