Consider the following premises. If Jennifer listens to a song, then James is rich. James is rich or Mary is not a nurse. If David plays a game, then Mary is a nurse. Jennifer is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: James is rich.
 From the fact that Jennifer is listening to a song we can infer that Jennifer is listening to a song or David is playing a game via addition. From the fact that James is rich or Mary is not a nurse we can infer that if Mary were a nurse, then James is rich via rewriting. From the fact that if David plays a game, then Mary is a nurse, and that if Mary were a nurse, then James is rich we can infer that if David plays a game, then James is rich via transitivity. Finally, from the fact that if Jennifer listens to a song, then James is rich, that if David plays a game, then James is rich, and that Jennifer is listening to a song or David is playing a game we can infer that James is rich via disjunction elimination. Therefore, the answer is yes.