Consider the following premises. For all y_2, y_2 will climb a mountain if and only if y_2 is poor. For all y_2, if y_2 drives a car, then y_2 is poor. There is at least one y_2 for which y_2 will not climb a mountain. For all y_2, if y_2 were poor, then y_2 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_2 for which y_2 will not drive a car.
 From the fact that for all y_2, y_2 will climb a mountain if and only if y_2 is poor, and that there is at least one y_2 for which y_2 will not climb a mountain we can infer that there is at least one y_2 for which y_2 is not poor via existential biconditional elimination. From the fact that for all y_2, if y_2 drives a car, then y_2 is poor, and that for all y_2, if y_2 were poor, then y_2 is driving a car we can infer that for all y_2, y_2 will drive a car if and only if y_2 is poor via universal biconditional introduction. Finally, from the fact that for all y_2, y_2 will drive a car if and only if y_2 is poor, and that there is at least one y_2 for which y_2 is not poor we can infer that there is at least one y_2 for which y_2 will not drive a car via existential biconditional elimination. Therefore, the answer is yes.