Consider the following premises. For all x_9, if x_9 were poor, then x_9 is a nurse. For all x_9, if x_9 were a nurse, then x_9 is poor. There is at least one x_9 for which x_9 is a nurse if and only if x_9 will drive a car. For all x_9, x_9 will work if and only if x_9 is poor. For all x_9, x_9 will not work. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 will drive a car.
 From the fact that for all x_9, if x_9 were poor, then x_9 is a nurse, and that for all x_9, if x_9 were a nurse, then x_9 is poor we can infer that for all x_9, x_9 is poor if and only if x_9 is a nurse via universal biconditional introduction. From the fact that for all x_9, x_9 will work if and only if x_9 is poor, and that for all x_9, x_9 will not work we can infer that for all x_9, x_9 is not poor via universal biconditional elimination. From the fact that for all x_9, x_9 is poor if and only if x_9 is a nurse, and that for all x_9, x_9 is not poor we can infer that for all x_9, x_9 is not a nurse via universal biconditional elimination. Finally, from the fact that there is at least one x_9 for which x_9 is a nurse if and only if x_9 will drive a car, and that for all x_9, x_9 is not a nurse we can infer that there is at least one x_9 for which x_9 will not drive a car via existential biconditional elimination, which contradicts that For all x_9, x_9 will drive a car. Therefore, the answer is no.