Consider the following premises. There is at least one x_4 for which if x_4 drives a car, then x_4 is a scientist. For all x_4, if x_4 drives a car, then x_4 is playing tennis. For all x_4, if x_4 plays tennis, then x_4 is driving a car. For all x_4, if x_4 were a scientist, then x_4 is playing tennis. Can we infer the following from them? For all x_4, if is not true that x_4 will play tennis if and only if x_4 will drive a car.
 From the fact that there is at least one x_4 for which if x_4 drives a car, then x_4 is a scientist, and that for all x_4, if x_4 were a scientist, then x_4 is playing tennis we can infer that there is at least one x_4 for which if x_4 drives a car, then x_4 is playing tennis. Finally, from the fact that for all x_4, if x_4 plays tennis, then x_4 is driving a car, and that for all x_4, if x_4 drives a car, then x_4 is playing tennis we can infer that for all x_4, x_4 will play tennis if and only if x_4 will drive a car, which contradicts that For all x_4, if is not true that x_4 will play tennis if and only if x_4 will drive a car. Therefore, the answer is no.