Consider the following premises. There is at least one x_8 for which if x_8 writes a letter, then x_8 is a janitor. For all x_8, if x_8 writes a letter, then x_8 is a janitor. For all x_8, if x_8 were a janitor, then x_8 is writing a letter. Can we infer the following from them? For all x_8, if x_8 writes a letter, then x_8 is a janitor.
That is one of the premises. Therefore, the answer is yes.