Consider the following premises. There is at least one x_8 for which x_8 is poor if and only if x_8 will climb a mountain. For all x_8, x_8 will work if and only if x_8 is poor. Can we infer the following from them? There is at least one x_8 for which if x_8 works, then x_8 is climbing a mountain.
 From the fact that for all x_8, x_8 will work if and only if x_8 is poor we can infer that for all x_8, if x_8 works, then x_8 is poor. From the fact that there is at least one x_8 for which x_8 is poor if and only if x_8 will climb a mountain we can infer that there is at least one x_8 for which if x_8 were poor, then x_8 is climbing a mountain. Finally, from the fact that for all x_8, if x_8 works, then x_8 is poor, and that there is at least one x_8 for which if x_8 were poor, then x_8 is climbing a mountain we can infer that there is at least one x_8 for which if x_8 works, then x_8 is climbing a mountain. Therefore, the answer is yes.