Consider the following premises. For all x_5, if x_5 drives a car, then x_5 is poor. For all x_5, x_5 will not drive a car. For all x_5, x_5 will drive a car if and only if x_5 is poor. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is not poor.
 From the fact that for all x_5, x_5 will drive a car if and only if x_5 is poor we can infer that for all x_5, if x_5 were poor, then x_5 is driving a car via universal biconditional elimination. From the fact that for all x_5, if x_5 drives a car, then x_5 is poor, and that for all x_5, if x_5 were poor, then x_5 is driving a car we can infer that for all x_5, x_5 will drive a car if and only if x_5 is poor via universal biconditional introduction. Finally, from the fact that for all x_5, x_5 will drive a car if and only if x_5 is poor, and that for all x_5, x_5 will not drive a car we can infer that for all x_5, x_5 is not poor via universal biconditional elimination. Therefore, the answer is yes.