Consider the following premises. James is a politician or Barbara is rich. If Barbara were rich, then Elisabeth is a musician. James is a politician if and only if David is excited. David is excited or Elisabeth is not a musician. Can we infer the following from them? If we can, name the inference rule being used: David is excited.
 From the fact that David is excited or Elisabeth is not a musician we can infer that if Elisabeth were a musician, then David is excited via rewriting. From the fact that if Barbara were rich, then Elisabeth is a musician, and that if Elisabeth were a musician, then David is excited we can infer that if Barbara were rich, then David is excited via transitivity. From the fact that James is a politician if and only if David is excited we can infer that if James were a politician, then David is excited via biconditional elimination. Finally, from the fact that if James were a politician, then David is excited, that if Barbara were rich, then David is excited, and that James is a politician or Barbara is rich we can infer that David is excited via disjunction elimination. Therefore, the answer is yes.