Consider the following premises. There is at least one y for which if y drives a car, then y is an astronaut. For all y, if y were an astronaut, then y is driving a car. For all y, if y were an astronaut, then y is driving a car. Can we infer the following from them? There is at least one y for which y is an astronaut if and only if y will drive a car.
 From the fact that there is at least one y for which if y drives a car, then y is an astronaut, and that for all y, if y were an astronaut, 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 is an astronaut. From the fact that there is at least one y for which y will drive a car if and only if y is an astronaut we can infer that there is at least one y for which if y drives a car, then y is an astronaut. Finally, from the fact that for all y, if y were an astronaut, then y is driving a car, and that there is at least one y for which if y drives a car, then y is an astronaut we can infer that there is at least one y for which y is an astronaut if and only if y will drive a car. Therefore, the answer is yes.