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 it is cold, then Sarah is listening to a song. It is raining if and only if it is cold. If Sarah listens to a song, then it is raining.
If it is cold, then it is raining can be inferred via the transitivity rule. If it rains, then it is cold can be inferred via the biconditional elimination rule. If it is cold, then it is raining can be inferred via the biconditional elimination rule.