Consider the following premises. For all x_1, if x_1 writes a letter, then x_1 is a nurse. For all x_1, if x_1 were a nurse, then x_1 is writing a letter. Can we infer the following from them? For all x_1, if x_1 writes a letter, then x_1 is a nurse.
That is one of the premises. Therefore, the answer is yes.