Consider the following premises. For all z, z will drink water if and only if z will climb a mountain. There is at least one z for which z will drink water or z will not climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z will climb a mountain if and only if z will drink 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 via universal biconditional elimination. From the fact that there is at least one z for which z will drink water or z will not climb a mountain we can infer that there is at least one z for which if z climbs a mountain, then z is drinking water via existential rewriting. Finally, from the fact that there is at least one z for which 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 there is at least one z for which z will climb a mountain if and only if z will drink water via existential biconditional introduction. Therefore, the answer is yes.