Consider the following premises. For all x_6, x_6 is a doctor if and only if x_6 will write a letter. There is at least one x_6 for which if x_6 were a soldier, then x_6 is a doctor. For all x_6, if x_6 writes a letter, then x_6 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is a doctor if and only if x_6 will write a letter.
That is one of the premises. Therefore, the answer is yes.