Consider the following premises. There is at least one x for which x will drive a car if and only if x is a doctor. For all x, x will drive a car. For all x, if x cooks, then x is a doctor. Can we infer the following from them? There is at least one x for which x is a doctor.
 From the fact that for all x, x will drive a car we can infer that for all x, x will drive a car or x will cook. From the fact that there is at least one x for which x will drive a car if and only if x is a doctor we can infer that there is at least one x for which if x drives a car, then x is a doctor. Finally, from the fact that there is at least one x for which if x drives a car, then x is a doctor, that for all x, if x cooks, then x is a doctor, and that for all x, x will drive a car or x will cook we can infer that there is at least one x for which x is a doctor. Therefore, the answer is yes.