Consider the following premises. For all x, if x were an office clerk, then x is a doctor. For all x, x is not a doctor. For all x, if x were a doctor, then x is a writer. For all x, if x were a writer, then x is an office clerk. Can we infer the following from them? For all x, if x were an office clerk, then x is a doctor.
That is one of the premises. Therefore, the answer is yes.