Consider the following premises. Barbara is not a politician. If John listens to a song, then John is climbing a mountain. John is climbing a mountain if and only if Barbara is a politician. Can we infer the following from them? If we can, name the inference rule being used: John is not listening to a song.
 From the fact that John is climbing a mountain if and only if Barbara is a politician we can infer that if John climbs a mountain, then Barbara is a politician via biconditional elimination. From the fact that if John climbs a mountain, then Barbara is a politician, and that Barbara is not a politician we can infer that John is not climbing a mountain via modus tollens. Finally, from the fact that if John listens to a song, then John is climbing a mountain, and that John is not climbing a mountain we can infer that John is not listening to a song via modus tollens. Therefore, the answer is yes.