Consider the following premises. For all z_3, if z_3 climbs a mountain, then z_3 is writing a letter. For all z_3, if z_3 were rich, then z_3 is climbing a mountain. For all z_3, if z_3 writes a letter, then z_3 is rich. Can we infer the following from them? There is at least one z_3 for which the fact that z_3 writes a letter does not imply that z_3 is climbing a mountain.
 From the fact that for all z_3, if z_3 writes a letter, then z_3 is rich, and that for all z_3, if z_3 were rich, then z_3 is climbing a mountain we can infer that for all z_3, if z_3 writes a letter, then z_3 is climbing a mountain. From the fact that for all z_3, if z_3 climbs a mountain, then z_3 is writing a letter, and that for all z_3, if z_3 writes a letter, then z_3 is climbing a mountain we can infer that for all z_3, z_3 will climb a mountain if and only if z_3 will write a letter. Finally, from the fact that for all z_3, z_3 will climb a mountain if and only if z_3 will write a letter we can infer that for all z_3, if z_3 writes a letter, then z_3 is climbing a mountain, which contradicts that There is at least one z_3 for which the fact that z_3 writes a letter does not imply that z_3 is climbing a mountain. Therefore, the answer is no.