Consider the following premises. There is at least one x_8 for which x_8 will play squash if and only if x_8 will climb a mountain. For all x_8, x_8 will play squash and x_8 will take a plane. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will not climb a mountain.
 From the fact that there is at least one x_8 for which x_8 will play squash 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 plays squash, then x_8 is climbing a mountain via existential biconditional elimination. From the fact that for all x_8, x_8 will play squash and x_8 will take a plane we can infer that for all x_8, x_8 will play squash via universal simplification. Finally, from the fact that there is at least one x_8 for which if x_8 plays squash, then x_8 is climbing a mountain, and that for all x_8, x_8 will play squash we can infer that there is at least one x_8 for which x_8 will climb a mountain via existential modus ponens, which contradicts that For all x_8, x_8 will not climb a mountain. Therefore, the answer is no.