Consider the following premises. For all x_9, x_9 is a doctor if and only if x_9 will play tennis. If it is cold, then Charles is a doctor. It is not cold. If Charles were a doctor, then it is cold. Can we infer the following from them? Charles is playing tennis.
 From the fact that for all x_9, x_9 is a doctor if and only if x_9 will play tennis we can infer that Charles is a doctor if and only if Charles is playing tennis. From the fact that if Charles were a doctor, then it is cold, and that if it is cold, then Charles is a doctor we can infer that Charles is a doctor if and only if it is cold. From the fact that Charles is a doctor if and only if it is cold, and that it is not cold we can infer that Charles is not a doctor. Finally, from the fact that Charles is a doctor if and only if Charles is playing tennis, and that Charles is not a doctor we can infer that Charles is not playing tennis, which contradicts that Charles is playing tennis. Therefore, the answer is no.