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