Consider the following premises. James is a mechanic if and only if Mary is playing squash. If Richard listens to a song, then James is a mechanic. If Mary plays squash, then Richard is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: Mary is playing squash if and only if Richard is listening to a song.
 From the fact that James is a mechanic if and only if Mary is playing squash we can infer that if James were a mechanic, then Mary is playing squash via biconditional elimination. From the fact that if Richard listens to a song, then James is a mechanic, and that if James were a mechanic, then Mary is playing squash we can infer that if Richard listens to a song, then Mary is playing squash via transitivity. Finally, from the fact that if Mary plays squash, then Richard is listening to a song, and that if Richard listens to a song, then Mary is playing squash we can infer that Mary is playing squash if and only if Richard is listening to a song via biconditional introduction. Therefore, the answer is yes.