Consider the following premises. For all x_9, x_9 will drive a car if and only if x_9 will cook. There is at least one x_9 for which x_9 will drive a car or x_9 will not cook. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which if x_9 drives a car, then x_9 is cooking.
 From the fact that there is at least one x_9 for which x_9 will drive a car or x_9 will not cook we can infer that there is at least one x_9 for which if x_9 cooks, then x_9 is driving a car via existential rewriting. From the fact that for all x_9, x_9 will drive a car if and only if x_9 will cook we can infer that for all x_9, if x_9 drives a car, then x_9 is cooking via universal biconditional elimination. From the fact that for all x_9, if x_9 drives a car, then x_9 is cooking, and that there is at least one x_9 for which if x_9 cooks, then x_9 is driving a car we can infer that there is at least one x_9 for which x_9 will drive a car if and only if x_9 will cook via existential biconditional introduction. Finally, from the fact that there is at least one x_9 for which x_9 will drive a car if and only if x_9 will cook we can infer that there is at least one x_9 for which if x_9 drives a car, then x_9 is cooking via existential biconditional elimination. Therefore, the answer is yes.