Consider the following premises. For all y_1, y_1 is a writer if and only if y_1 will drive a car. For all y_1, y_1 is not a writer. For all y_1, y_1 will drive a car if and only if y_1 is a writer. Can we infer the following from them? If we can, name the inference rule being used: For all y_1, y_1 will not drive a car.
 From the fact that for all y_1, y_1 will drive a car if and only if y_1 is a writer we can infer that for all y_1, if y_1 were a writer, then y_1 is driving a car via universal biconditional elimination. From the fact that for all y_1, y_1 is a writer if and only if y_1 will drive a car we can infer that for all y_1, if y_1 drives a car, then y_1 is a writer via universal biconditional elimination. From the fact that for all y_1, if y_1 drives a car, then y_1 is a writer, and that for all y_1, if y_1 were a writer, then y_1 is driving a car we can infer that for all y_1, y_1 will drive a car if and only if y_1 is a writer via universal biconditional introduction. Finally, from the fact that for all y_1, y_1 will drive a car if and only if y_1 is a writer, and that for all y_1, y_1 is not a writer we can infer that for all y_1, y_1 will not drive a car via universal biconditional elimination. Therefore, the answer is yes.