Consider the following premises. For all x_9, if x_9 were a janitor, then x_9 is writing a letter. For all x_9, x_9 is a janitor or x_9 will not write a letter. For all x_9, if x_9 writes a letter, then x_9 is a janitor. Can we infer the following from them? For all x_9, x_9 will write a letter if and only if x_9 is a janitor.
 From the fact that for all x_9, if x_9 were a janitor, then x_9 is writing a letter, and that for all x_9, if x_9 writes a letter, then x_9 is a janitor we can infer that for all x_9, x_9 is a janitor if and only if x_9 will write a letter. From the fact that for all x_9, x_9 is a janitor if and only if x_9 will write a letter we can infer that for all x_9, if x_9 were a janitor, then x_9 is writing a letter. From the fact that for all x_9, x_9 is a janitor or x_9 will not write a letter we can infer that for all x_9, if x_9 writes a letter, then x_9 is a janitor. Finally, from the fact that for all x_9, if x_9 writes a letter, then x_9 is a janitor, and that for all x_9, if x_9 were a janitor, then x_9 is writing a letter we can infer that for all x_9, x_9 will write a letter if and only if x_9 is a janitor. Therefore, the answer is yes.