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