Consider the following premises. If Joseph were a doctor, then it is late. It is snowing if and only if it is late. If it snows, then Joseph is a doctor. Can we infer the following from them? If it is late, then Joseph is a doctor.
 From the fact that it is snowing if and only if it is late we can infer that if it is late, then it is snowing. Finally, from the fact that if it is late, then it is snowing, and that if it snows, then Joseph is a doctor we can infer that if it is late, then Joseph is a doctor. Therefore, the answer is yes.