Consider the following premises. For all y, if y were a janitor, then y is playing tennis. There is at least one y for which y will drive a car. For all y, if y plays tennis, then y is a janitor. For all y, y is a janitor or y will not drive a car. Can we infer the following from them? There is at least one y for which y will play tennis.
 From the fact that for all y, y is a janitor or y will not drive a car we can infer that for all y, if y drives a car, then y is a janitor. From the fact that for all y, if y plays tennis, then y is a janitor, and that for all y, if y were a janitor, then y is playing tennis we can infer that for all y, y will play tennis if and only if y is a janitor. From the fact that for all y, y will play tennis if and only if y is a janitor we can infer that for all y, if y were a janitor, then y is playing tennis. From the fact that for all y, if y drives a car, then y is a janitor, and that there is at least one y for which y will drive a car we can infer that there is at least one y for which y is a janitor. Finally, from the fact that for all y, if y were a janitor, then y is playing tennis, and that there is at least one y for which y is a janitor we can infer that there is at least one y for which y will play tennis. Therefore, the answer is yes.