Consider the following premises. There is at least one x_10 for which x_10 is a nurse if and only if x_10 will drive a car. For all x_10, x_10 will play tennis if and only if x_10 will drive a car. For all x_10, x_10 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 will not drive a car.
 From the fact that there is at least one x_10 for which x_10 is a nurse if and only if x_10 will drive a car we can infer that there is at least one x_10 for which if x_10 were a nurse, then x_10 is driving a car via existential biconditional elimination. From the fact that for all x_10, x_10 will play tennis we can infer that for all x_10, x_10 will play tennis or x_10 is a nurse via universal addition. From the fact that for all x_10, x_10 will play tennis if and only if x_10 will drive a car we can infer that for all x_10, if x_10 plays tennis, then x_10 is driving a car via universal biconditional elimination. Finally, from the fact that for all x_10, if x_10 plays tennis, then x_10 is driving a car, that there is at least one x_10 for which if x_10 were a nurse, then x_10 is driving a car, and that for all x_10, x_10 will play tennis or x_10 is a nurse we can infer that there is at least one x_10 for which x_10 will drive a car via existential disjunction elimination, which contradicts that For all x_10, x_10 will not drive a car. Therefore, the answer is no.