Consider the following premises. For all z_2, if z_2 writes a letter, then z_2 is rich. For all z_2, if z_2 were bored, then z_2 is climbing a mountain. For all z_2, z_2 will write a letter. There is at least one z_2 for which z_2 is bored if and only if z_2 is rich. Can we infer the following from them? There is at least one z_2 for which z_2 will climb a mountain.
 From the fact that there is at least one z_2 for which z_2 is bored if and only if z_2 is rich we can infer that there is at least one z_2 for which if z_2 were rich, then z_2 is bored. From the fact that for all z_2, if z_2 writes a letter, then z_2 is rich, and that there is at least one z_2 for which if z_2 were rich, then z_2 is bored we can infer that there is at least one z_2 for which if z_2 writes a letter, then z_2 is bored. From the fact that there is at least one z_2 for which if z_2 writes a letter, then z_2 is bored, and that for all z_2, if z_2 were bored, then z_2 is climbing a mountain we can infer that there is at least one z_2 for which if z_2 writes a letter, then z_2 is climbing a mountain. Finally, from the fact that there is at least one z_2 for which if z_2 writes a letter, then z_2 is climbing a mountain, and that for all z_2, z_2 will write a letter we can infer that there is at least one z_2 for which z_2 will climb a mountain. Therefore, the answer is yes.