Consider the following premises. There is at least one x_5 for which if x_5 were a lawyer, then x_5 is climbing a mountain. For all x_5, x_5 will climb a mountain if and only if x_5 is a lawyer. For all x_5, x_5 is not a lawyer. Can we infer the following from them? For all x_5, x_5 will climb a mountain.
 From the fact that for all x_5, x_5 will climb a mountain if and only if x_5 is a lawyer we can infer that for all x_5, if x_5 climbs a mountain, then x_5 is a lawyer. From the fact that for all x_5, if x_5 climbs a mountain, then x_5 is a lawyer, and that there is at least one x_5 for which if x_5 were a lawyer, then x_5 is climbing a mountain we can infer that there is at least one x_5 for which x_5 will climb a mountain if and only if x_5 is a lawyer. Finally, from the fact that there is at least one x_5 for which x_5 will climb a mountain if and only if x_5 is a lawyer, and that for all x_5, x_5 is not a lawyer we can infer that there is at least one x_5 for which x_5 will not climb a mountain, which contradicts that For all x_5, x_5 will climb a mountain. Therefore, the answer is no.