Consider the following premises. If Jennifer were poor, then John is playing a game. James is a carpenter or John is not playing a game. Jennifer is poor or James is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is poor if and only if James is a carpenter.
 From the fact that James is a carpenter or John is not playing a game we can infer that if John plays a game, then James is a carpenter via rewriting. From the fact that if Jennifer were poor, then John is playing a game, and that if John plays a game, then James is a carpenter we can infer that if Jennifer were poor, then James is a carpenter via transitivity. From the fact that Jennifer is poor or James is not a carpenter we can infer that if James were a carpenter, then Jennifer is poor via rewriting. Finally, from the fact that if Jennifer were poor, then James is a carpenter, and that if James were a carpenter, then Jennifer is poor we can infer that Jennifer is poor if and only if James is a carpenter via biconditional introduction. Therefore, the answer is yes.