Consider the following premises. It is late if and only if Thomas is climbing a mountain. Thomas is climbing a mountain if and only if Robert is a poet. Can we infer the following from them? If we can, name the inference rule being used: If Robert were a poet, then it is late.
 From the fact that it is late if and only if Thomas is climbing a mountain we can infer that if Thomas climbs a mountain, then it is late via biconditional elimination. From the fact that Thomas is climbing a mountain if and only if Robert is a poet we can infer that if Robert were a poet, then Thomas is climbing a mountain via biconditional elimination. Finally, from the fact that if Robert were a poet, then Thomas is climbing a mountain, and that if Thomas climbs a mountain, then it is late we can infer that if Robert were a poet, then it is late via transitivity. Therefore, the answer is yes.