Consider the following premises. If Thomas were a lawyer, then David is climbing a mountain. If Michael were a bartender, then David is climbing a mountain. Thomas is a lawyer if and only if David is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: If Michael were a bartender, then Thomas is a lawyer.
 From the fact that Thomas is a lawyer if and only if David is climbing a mountain we can infer that if David climbs a mountain, then Thomas is a lawyer via biconditional elimination. From the fact that if David climbs a mountain, then Thomas is a lawyer, and that if Thomas were a lawyer, then David is climbing a mountain we can infer that David is climbing a mountain if and only if Thomas is a lawyer via biconditional introduction. From the fact that David is climbing a mountain if and only if Thomas is a lawyer we can infer that if David climbs a mountain, then Thomas is a lawyer via biconditional elimination. Finally, from the fact that if Michael were a bartender, then David is climbing a mountain, and that if David climbs a mountain, then Thomas is a lawyer we can infer that if Michael were a bartender, then Thomas is a lawyer via transitivity. Therefore, the answer is yes.