Consider the following premises. For all x, if x drives a car, then x is playing a game. There is at least one x for which x will play a game if and only if x is a politician. For all x, if x plays a game, then x is driving a car. Can we infer the following from them? There is at least one x for which if x were a politician, then x is driving a car.
 From the fact that there is at least one x for which x will play a game if and only if x is a politician we can infer that there is at least one x for which if x were a politician, then x is playing a game. From the fact that for all x, if x plays a game, then x is driving a car, and that for all x, if x drives a car, then x is playing a game we can infer that for all x, x will play a game if and only if x will drive a car. From the fact that for all x, x will play a game if and only if x will drive a car we can infer that for all x, if x plays a game, then x is driving a car. Finally, from the fact that there is at least one x for which if x were a politician, then x is playing a game, and that for all x, if x plays a game, then x is driving a car we can infer that there is at least one x for which if x were a politician, then x is driving a car. Therefore, the answer is yes.