Consider the following premises. For all y, y will take a plane or y will not drive a car. There is at least one y for which if y drives a car, then y is taking a plane. For all y, y will not take a plane. For all y, if y takes a plane, then y 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 for which y will not drive a car.
 From the fact that there is at least one y for which if y drives a car, then y is taking a plane, and that for all y, if y takes a plane, then y is driving a car we can infer that there is at least one y for which y will drive a car if and only if y will take a plane via existential biconditional introduction. From the fact that for all y, y will take a plane or y will not drive a car we can infer that for all y, if y drives a car, then y is taking a plane via universal rewriting. From the fact that there is at least one y for which y will drive a car if and only if y will take a plane we can infer that there is at least one y for which if y takes a plane, then y is driving a car via existential biconditional elimination. From the fact that there is at least one y for which if y takes a plane, then y is driving a car, and that for all y, if y drives a car, then y is taking a plane we can infer that there is at least one y for which y will take a plane if and only if y will drive a car via existential biconditional introduction. Finally, from the fact that there is at least one y for which y will take a plane if and only if y will drive a car, and that for all y, y will not take a plane we can infer that there is at least one y for which y will not drive a car via existential biconditional elimination. Therefore, the answer is yes.