Consider the following premises. John is climbing a mountain or it is not raining. John is climbing a mountain if and only if it is raining. Can we infer the following from them? If we can, name the inference rule being used: It is raining if and only if John is climbing a mountain.
 From the fact that John is climbing a mountain if and only if it is raining we can infer that if John climbs a mountain, then it is raining via biconditional elimination. From the fact that John is climbing a mountain or it is not raining we can infer that if it rains, then John is climbing a mountain via rewriting. Finally, from the fact that if it rains, then John is climbing a mountain, and that if John climbs a mountain, then it is raining we can infer that it is raining if and only if John is climbing a mountain via biconditional introduction. Therefore, the answer is yes.