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