Consider the following premises. For all x_12, x_12 will listen to a song if and only if x_12 will write a letter. Charles is listening to a song if and only if Charles is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: Charles is writing a letter if and only if Charles is listening to a song.
 From the fact that for all x_12, x_12 will listen to a song if and only if x_12 will write a letter we can infer that Charles is listening to a song if and only if Charles is writing a letter via universal instantiation. From the fact that Charles is listening to a song if and only if Charles is writing a letter we can infer that if Charles listens to a song, then Charles is writing a letter via biconditional elimination. From the fact that Charles is listening to a song if and only if Charles is writing a letter we can infer that if Charles writes a letter, then Charles is listening to a song via biconditional elimination. Finally, from the fact that if Charles writes a letter, then Charles is listening to a song, and that if Charles listens to a song, then Charles is writing a letter we can infer that Charles is writing a letter if and only if Charles is listening to a song via biconditional introduction. Therefore, the answer is yes.