Consider the following premises. For all z_2, z_2 is not a sailor. For all z_2, z_2 will climb a mountain if and only if z_2 is a sailor. For all z_2, z_2 will write a letter if and only if z_2 will climb a mountain. There is at least one z_2 for which if z_2 were poor, then z_2 is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: For all z_2, z_2 is poor.
 From the fact that for all z_2, z_2 will climb a mountain if and only if z_2 is a sailor, and that for all z_2, z_2 is not a sailor we can infer that for all z_2, z_2 will not climb a mountain via universal biconditional elimination. From the fact that for all z_2, z_2 will write a letter if and only if z_2 will climb a mountain, and that for all z_2, z_2 will not climb a mountain we can infer that for all z_2, z_2 will not write a letter via universal biconditional elimination. Finally, from the fact that there is at least one z_2 for which if z_2 were poor, then z_2 is writing a letter, and that for all z_2, z_2 will not write a letter we can infer that there is at least one z_2 for which z_2 is not poor via existential modus tollens, which contradicts that For all z_2, z_2 is poor. Therefore, the answer is no.