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