Consider the following premises. Susan is not a cashier. If Patricia were sad, then it is cold. If it is cold, then Patricia is sad. If Patricia were sad, then Susan is a cashier. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that if Patricia were sad, then Susan is a cashier, and that Susan is not a cashier we can infer that Patricia is not sad via modus tollens. From the fact that if it is cold, then Patricia is sad, and that if Patricia were sad, then it is cold we can infer that it is cold if and only if Patricia is sad via biconditional introduction. Finally, from the fact that it is cold if and only if Patricia is sad, and that Patricia is not sad we can infer that it is not cold via biconditional elimination. Therefore, the answer is yes.