Consider the following premises. For all z, if z climbs a mountain, then z is cooking. For all z, z will cook if and only if z will climb a mountain. Can we infer the following from them? There is at least one z for which the fact that z climbs a mountain does not imply that z is cooking.
 From the fact that for all z, z will cook if and only if z will climb a mountain we can infer that for all z, if z cooks, then z is climbing a mountain. From the fact that for all z, if z climbs a mountain, then z is cooking, and that for all z, if z cooks, then z is climbing a mountain we can infer that for all z, z will climb a mountain if and only if z will cook. Finally, from the fact that for all z, z will climb a mountain if and only if z will cook we can infer that for all z, if z climbs a mountain, then z is cooking, which contradicts that There is at least one z for which the fact that z climbs a mountain does not imply that z is cooking. Therefore, the answer is no.