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: Elisabeth is a politician if and only if Jessica is listening to a song. If it is cold, then Elisabeth is a politician. It is cold or Michael is not climbing a mountain. Jessica is not listening to a song.
If Michael climbs a mountain, then it is cold can be inferred via the rewriting rule. If Elisabeth were a politician, then Jessica is listening to a song can be inferred via the biconditional elimination rule. If Jessica listens to a song, then Elisabeth is a politician can be inferred via the biconditional elimination rule. Elisabeth is not a politician can be inferred via the biconditional elimination rule.