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