Consider the following premises. For all x_7, if x_7 climbs a mountain, then x_7 is driving a car. For all x_7, x_7 will drive a car if and only if x_7 will play squash. There is at least one x_7 for which x_7 will climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will drive a car.
 From the fact that for all x_7, x_7 will drive a car if and only if x_7 will play squash we can infer that for all x_7, if x_7 plays squash, then x_7 is driving a car via universal biconditional elimination. From the fact that there is at least one x_7 for which x_7 will climb a mountain we can infer that there is at least one x_7 for which x_7 will climb a mountain or x_7 will play squash via existential addition. Finally, from the fact that for all x_7, if x_7 climbs a mountain, then x_7 is driving a car, that for all x_7, if x_7 plays squash, then x_7 is driving a car, and that there is at least one x_7 for which x_7 will climb a mountain or x_7 will play squash we can infer that there is at least one x_7 for which x_7 will drive a car via existential disjunction elimination. Therefore, the answer is yes.