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