Consider the following premises. For all x, if x were rich, then x is listening to a song. James is not rich. James is rich if and only if James is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: James is listening to a song.
 From the fact that for all x, if x were rich, then x is listening to a song we can infer that if James were rich, then James is listening to a song via universal instantiation. From the fact that James is rich if and only if James is listening to a song we can infer that if James listens to a song, then James is rich via biconditional elimination. From the fact that if James were rich, then James is listening to a song, and that if James listens to a song, then James is rich we can infer that James is rich if and only if James is listening to a song via biconditional introduction. Finally, from the fact that James is rich if and only if James is listening to a song, and that James is not rich we can infer that James is not listening to a song via biconditional elimination, which contradicts that James is listening to a song. Therefore, the answer is no.