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