Consider the following premises. For all x_9, x_9 is a musician if and only if x_9 will write a letter. For all x_9, x_9 is not a musician. For all x_9, x_9 will write a letter if and only if x_9 is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 will not write a letter.
 From the fact that for all x_9, x_9 will write a letter if and only if x_9 is a musician we can infer that for all x_9, if x_9 were a musician, then x_9 is writing a letter via universal biconditional elimination. From the fact that for all x_9, x_9 is a musician if and only if x_9 will write a letter we can infer that for all x_9, if x_9 writes a letter, then x_9 is a musician via universal biconditional elimination. From the fact that for all x_9, if x_9 writes a letter, then x_9 is a musician, and that for all x_9, if x_9 were a musician, 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 musician via universal biconditional introduction. Finally, from the fact that for all x_9, x_9 will write a letter if and only if x_9 is a musician, and that for all x_9, x_9 is not a musician we can infer that for all x_9, x_9 will not write a letter via universal biconditional elimination. Therefore, the answer is yes.