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