Consider the following premises. If Patricia were bored, then David is working. David is not working. If it is cold, then Patricia is bored. If David works, then it is cold. Can we infer the following from them? If we can, name the inference rule being used: It is cold.
 From the fact that if it is cold, then Patricia is bored, and that if Patricia were bored, then David is working we can infer that if it is cold, then David is working via transitivity. From the fact that if David works, then it is cold, and that if it is cold, then David is working we can infer that David is working if and only if it is cold via biconditional introduction. Finally, from the fact that David is working if and only if it is cold, and that David is not working we can infer that it is not cold via biconditional elimination, which contradicts that It is cold. Therefore, the answer is no.