Consider the following premises. If James were an artist, then Patricia is playing squash. If Barbara were poor, then it is cloudy. Barbara is poor or Patricia is not playing squash. If it is cloudy, then James is an artist. Can we infer the following from them? If we can, name the inference rule being used: James is an artist if and only if Barbara is poor.
 From the fact that Barbara is poor or Patricia is not playing squash we can infer that if Patricia plays squash, then Barbara is poor via rewriting. From the fact that if Barbara were poor, then it is cloudy, and that if it is cloudy, then James is an artist we can infer that if Barbara were poor, then James is an artist via transitivity. From the fact that if James were an artist, then Patricia is playing squash, and that if Patricia plays squash, then Barbara is poor we can infer that if James were an artist, then Barbara is poor via transitivity. Finally, from the fact that if James were an artist, then Barbara is poor, and that if Barbara were poor, then James is an artist we can infer that James is an artist if and only if Barbara is poor via biconditional introduction. Therefore, the answer is yes.