Consider the following premises. For all x, if x were a doctor, then x is a scientist. There is at least one x for which x is happy or x is not a scientist. For all x, x is a doctor or x is not happy. Can we infer the following from them? There is at least one x for which if x were a scientist, then x is a doctor.
 From the fact that for all x, x is a doctor or x is not happy we can infer that for all x, if x were happy, then x is a doctor. From the fact that there is at least one x for which x is happy or x is not a scientist we can infer that there is at least one x for which if x were a scientist, then x is happy. Finally, from the fact that there is at least one x for which if x were a scientist, then x is happy, and that for all x, if x were happy, then x is a doctor we can infer that there is at least one x for which if x were a scientist, then x is a doctor. Therefore, the answer is yes.