Consider the following premises. If James were a soldier, then it is cold. If it is cold, then Linda is working. If Linda works, then Charles is climbing a mountain. If Linda works, then it is cold. Can we infer the following from them? If we can, name the inference rule being used: If James were a soldier, then Charles is climbing a mountain.
 From the fact that if it is cold, then Linda is working, and that if Linda works, then it is cold we can infer that it is cold if and only if Linda is working via biconditional introduction. From the fact that it is cold if and only if Linda is working we can infer that if it is cold, then Linda is working via biconditional elimination. From the fact that if it is cold, then Linda is working, and that if Linda works, then Charles is climbing a mountain we can infer that if it is cold, then Charles is climbing a mountain via transitivity. Finally, from the fact that if James were a soldier, then it is cold, and that if it is cold, then Charles is climbing a mountain we can infer that if James were a soldier, then Charles is climbing a mountain via transitivity. Therefore, the answer is yes.