Consider the following premises. If it is cloudy, then Barbara is a sailor. It is snowing if and only if Thomas is climbing a mountain. Thomas is climbing a mountain if and only if it is cloudy. If Barbara were a sailor, then it is snowing. Can we infer the following from them? If we can, name the inference rule being used: If is not true that it is cloudy if and only if Thomas is climbing a mountain.
 From the fact that if it is cloudy, then Barbara is a sailor, and that if Barbara were a sailor, then it is snowing we can infer that if it is cloudy, then it is snowing via transitivity. From the fact that Thomas is climbing a mountain if and only if it is cloudy we can infer that if Thomas climbs a mountain, then it is cloudy via biconditional elimination. From the fact that it is snowing if and only if Thomas is climbing a mountain we can infer that if it snows, then Thomas is climbing a mountain via biconditional elimination. From the fact that if it is cloudy, then it is snowing, and that if it snows, then Thomas is climbing a mountain we can infer that if it is cloudy, then Thomas is climbing a mountain via transitivity. Finally, from the fact that if it is cloudy, then Thomas is climbing a mountain, and that if Thomas climbs a mountain, then it is cloudy we can infer that it is cloudy if and only if Thomas is climbing a mountain via biconditional introduction, which contradicts that If is not true that it is cloudy if and only if Thomas is climbing a mountain. Therefore, the answer is no.