Consider the following premises. David is playing tennis if and only if Michael is bored. David is not climbing a mountain. David is playing tennis if and only if David is climbing a mountain. Linda is sad. Can we infer the following from them? If we can, name the inference rule being used: Michael is not bored.
 From the fact that David is playing tennis if and only if David is climbing a mountain, and that David is not climbing a mountain we can infer that David is not playing tennis via biconditional elimination. Finally, from the fact that David is playing tennis if and only if Michael is bored, and that David is not playing tennis we can infer that Michael is not bored via biconditional elimination. Therefore, the answer is yes.