Consider the following premises. For all x_6, x_6 is fast if and only if x_6 is poor. For all x_6, x_6 is not poor. For all x_6, if x_6 were fast, then x_6 is climbing a mountain. There is at least one x_6 for which if x_6 climbs a mountain, then x_6 is fast. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will climb a mountain.
 From the fact that for all x_6, x_6 is fast if and only if x_6 is poor, and that for all x_6, x_6 is not poor we can infer that for all x_6, x_6 is not fast via universal biconditional elimination. From the fact that there is at least one x_6 for which if x_6 climbs a mountain, then x_6 is fast, and that for all x_6, if x_6 were fast, then x_6 is climbing a mountain we can infer that there is at least one x_6 for which x_6 will climb a mountain if and only if x_6 is fast via existential biconditional introduction. Finally, from the fact that there is at least one x_6 for which x_6 will climb a mountain if and only if x_6 is fast, and that for all x_6, x_6 is not fast we can infer that there is at least one x_6 for which x_6 will not climb a mountain via existential biconditional elimination, which contradicts that For all x_6, x_6 will climb a mountain. Therefore, the answer is no.