What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: If Barbara climbs a mountain, then it is cloudy. If James were excited, then Barbara is climbing a mountain. It is cloudy if and only if Karen is writing a letter.
If James were excited, then it is cloudy can be inferred via the transitivity rule. If it is cloudy, then Karen is writing a letter can be inferred via the biconditional elimination rule. If Karen writes a letter, then it is cloudy can be inferred via the biconditional elimination rule.