Consider the following premises. For all x_7, if x_7 were sad, then x_7 is not a doctor. For all x_7, x_7 is a doctor. For all x_7, x_7 is sad if and only if x_7 is a scientist. For all x_7, if x_7 climbs a mountain, then x_7 is a scientist. For all x_7, if x_7 were a scientist, then x_7 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will not climb a mountain.
 From the fact that for all x_7, if x_7 were sad, then x_7 is not a doctor, and that for all x_7, x_7 is a doctor we can infer that for all x_7, x_7 is not sad via universal modus tollens. From the fact that for all x_7, if x_7 climbs a mountain, then x_7 is a scientist, and that for all x_7, if x_7 were a scientist, then x_7 is climbing a mountain we can infer that for all x_7, x_7 will climb a mountain if and only if x_7 is a scientist via universal biconditional introduction. From the fact that for all x_7, x_7 is sad if and only if x_7 is a scientist, and that for all x_7, x_7 is not sad we can infer that for all x_7, x_7 is not a scientist via universal biconditional elimination. Finally, from the fact that for all x_7, x_7 will climb a mountain if and only if x_7 is a scientist, and that for all x_7, x_7 is not a scientist we can infer that for all x_7, x_7 will not climb a mountain via universal biconditional elimination. Therefore, the answer is yes.