Consider the following premises. For all y_1, if y_1 plays tennis, then y_1 is a doctor. For all y_1, if y_1 plays tennis, then y_1 is a doctor. For all y_1, y_1 is a doctor if and only if y_1 will play tennis. Can we infer the following from them? There is at least one y_1 for which the fact that y_1 plays tennis does not imply that y_1 is a doctor.
 From the fact that for all y_1, y_1 is a doctor if and only if y_1 will play tennis we can infer that for all y_1, if y_1 were a doctor, then y_1 is playing tennis. From the fact that for all y_1, if y_1 were a doctor, then y_1 is playing tennis, and that for all y_1, if y_1 plays tennis, then y_1 is a doctor we can infer that for all y_1, y_1 is a doctor if and only if y_1 will play tennis. From the fact that for all y_1, y_1 is a doctor if and only if y_1 will play tennis we can infer that for all y_1, if y_1 were a doctor, then y_1 is playing tennis. From the fact that for all y_1, if y_1 plays tennis, then y_1 is a doctor, and that for all y_1, if y_1 were a doctor, then y_1 is playing tennis we can infer that for all y_1, y_1 will play tennis if and only if y_1 is a doctor. Finally, from the fact that for all y_1, y_1 will play tennis if and only if y_1 is a doctor we can infer that for all y_1, if y_1 plays tennis, then y_1 is a doctor, which contradicts that There is at least one y_1 for which the fact that y_1 plays tennis does not imply that y_1 is a doctor. Therefore, the answer is no.