Consider the following premises. For all x_9, x_9 will play squash or x_9 is a politician. There is at least one x_9 for which if x_9 plays squash, then x_9 is climbing a mountain. For all x_9, x_9 will not climb a mountain. For all x_9, if x_9 climbs a mountain, then x_9 is playing squash. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 is a politician.
 From the fact that there is at least one x_9 for which if x_9 plays squash, then x_9 is climbing a mountain, and that for all x_9, if x_9 climbs a mountain, then x_9 is playing squash we can infer that there is at least one x_9 for which x_9 will play squash if and only if x_9 will climb a mountain via existential biconditional introduction. From the fact that there is at least one x_9 for which x_9 will play squash if and only if x_9 will climb a mountain, and that for all x_9, x_9 will not climb a mountain we can infer that there is at least one x_9 for which x_9 will not play squash via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 will play squash or x_9 is a politician, and that there is at least one x_9 for which x_9 will not play squash we can infer that there is at least one x_9 for which x_9 is a politician via existential disjunctive syllogism. Therefore, the answer is yes.