Consider the following premises. If John were not a cashier, then John is writing a letter. Barbara is driving a car if and only if John is a cashier. Barbara is not driving a car. If John writes a letter, 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 Barbara is driving a car if and only if John is a cashier, and that Barbara is not driving a car we can infer that John is not a cashier via biconditional elimination. From the fact that if John were not a cashier, then John is writing a letter, and that if John writes a letter, then it is cold we can infer that if John were not a cashier, then it is cold via transitivity. Finally, from the fact that if John were not a cashier, then it is cold, and that John is not a cashier we can infer that it is cold via modus ponens. Therefore, the answer is yes.