Consider the following premises. If Sarah were fast, then Barbara is happy. Barbara is not happy. If Sarah were not fast, then it is cold. If Barbara were happy, then Sarah is fast. 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 Barbara were happy, then Sarah is fast, and that if Sarah were fast, then Barbara is happy we can infer that Barbara is happy if and only if Sarah is fast via biconditional introduction. From the fact that Barbara is happy if and only if Sarah is fast, and that Barbara is not happy we can infer that Sarah is not fast via biconditional elimination. Finally, from the fact that if Sarah were not fast, then it is cold, and that Sarah is not fast we can infer that it is cold via modus ponens, which contradicts that It is not cold. Therefore, the answer is no.