Consider the following premises. For all x_6, x_6 will listen to a song or x_6 will not write a letter. For all x_6, x_6 will write a letter if and only if x_6 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will listen to a song if and only if x_6 will write a letter.
 From the fact that for all x_6, x_6 will listen to a song or x_6 will not write a letter we can infer that for all x_6, if x_6 writes a letter, then x_6 is listening to a song via universal rewriting. From the fact that for all x_6, x_6 will write a letter if and only if x_6 will listen to a song we can infer that for all x_6, if x_6 listens to a song, then x_6 is writing a letter via universal biconditional elimination. Finally, from the fact that for all x_6, if x_6 listens to a song, then x_6 is writing a letter, and that for all x_6, if x_6 writes a letter, then x_6 is listening to a song we can infer that for all x_6, x_6 will listen to a song if and only if x_6 will write a letter via universal biconditional introduction. Therefore, the answer is yes.