Consider the following premises. For all x_7, x_7 is excited. For all x_7, if x_7 were poor, then x_7 is not excited. For all x_7, if x_7 were poor, then x_7 is driving a car. For all x_7, x_7 will drive a car if and only if x_7 is poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will drive a car.
 From the fact that for all x_7, if x_7 were poor, then x_7 is not excited, and that for all x_7, x_7 is excited we can infer that for all x_7, x_7 is not poor via universal modus tollens. From the fact that for all x_7, x_7 will drive a car if and only if x_7 is poor we can infer that for all x_7, if x_7 drives a car, then x_7 is poor via universal biconditional elimination. From the fact that for all x_7, if x_7 were poor, then x_7 is driving a car, and that for all x_7, if x_7 drives a car, then x_7 is poor we can infer that for all x_7, x_7 is poor if and only if x_7 will drive a car via universal biconditional introduction. Finally, from the fact that for all x_7, x_7 is poor if and only if x_7 will drive a car, and that for all x_7, x_7 is not poor we can infer that for all x_7, x_7 will not drive a car via universal biconditional elimination, which contradicts that There is at least one x_7 for which x_7 will drive a car. Therefore, the answer is no.