Consider the following premises. For all x_2, if x_2 cooks, then x_2 is a doctor. For all x_2, x_2 is not a doctor. For all x_2, if x_2 were a doctor, then x_2 is cooking. There is at least one x_2 for which x_2 will cook or x_2 will drive a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, if x_2 were a doctor, then x_2 is cooking.
That is one of the premises. Therefore, the answer is yes.