Consider the following premises. David is poor if and only if Robert is happy. If David were poor, then it is not late. Sarah is climbing a mountain if and only if Robert is happy. It is late. Can we infer the following from them? If we can, name the inference rule being used: Sarah is not climbing a mountain.
 From the fact that if David were poor, then it is not late, and that it is late we can infer that David is not poor via modus tollens. From the fact that David is poor if and only if Robert is happy, and that David is not poor we can infer that Robert is not happy via biconditional elimination. Finally, from the fact that Sarah is climbing a mountain if and only if Robert is happy, and that Robert is not happy we can infer that Sarah is not climbing a mountain via biconditional elimination. Therefore, the answer is yes.