Consider the following premises. For all x_9, x_9 will drive a car if and only if x_9 will play squash. For all x_9, x_9 will drive a car if and only if x_9 will play squash. 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 the fact that x_9 drives a car does not imply that x_9 is playing squash.
 From the fact that for all x_9, x_9 will drive a car if and only if x_9 will play squash we can infer that for all x_9, if x_9 plays squash, then x_9 is driving a car via universal biconditional elimination. From the fact that for all x_9, x_9 will drive a car if and only if x_9 will play squash we can infer that for all x_9, if x_9 drives a car, then x_9 is playing squash via universal biconditional elimination. From the fact that for all x_9, if x_9 drives a car, then x_9 is playing squash, and that for all x_9, if x_9 plays squash, then x_9 is driving a car we can infer that for all x_9, x_9 will drive a car if and only if x_9 will play squash via universal biconditional introduction. Finally, from the fact that for all x_9, x_9 will drive a car if and only if x_9 will play squash we can infer that for all x_9, if x_9 drives a car, then x_9 is playing squash via universal biconditional elimination, which contradicts that There is at least one x_9 for which the fact that x_9 drives a car does not imply that x_9 is playing squash. Therefore, the answer is no.