Consider the following premises. For all x_2, x_2 will take a plane if and only if x_2 will climb a mountain. For all x_2, x_2 will not cook. For all x_2, x_2 will take a plane if and only if x_2 will cook. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 will not climb a mountain.
 From the fact that for all x_2, x_2 will take a plane if and only if x_2 will cook we can infer that for all x_2, if x_2 takes a plane, then x_2 is cooking via universal biconditional elimination. From the fact that for all x_2, if x_2 takes a plane, then x_2 is cooking, and that for all x_2, x_2 will not cook we can infer that for all x_2, x_2 will not take a plane via universal modus tollens. Finally, from the fact that for all x_2, x_2 will take a plane if and only if x_2 will climb a mountain, and that for all x_2, x_2 will not take a plane we can infer that for all x_2, x_2 will not climb a mountain via universal biconditional elimination. Therefore, the answer is yes.