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 late, then it is raining. Charles is playing tennis if and only if it is raining. If Joseph climbs a mountain, then it is late.
If Joseph climbs a mountain, then it is raining can be inferred via the transitivity rule. If Charles plays tennis, then it is raining can be inferred via the biconditional elimination rule. If it rains, then Charles is playing tennis can be inferred via the biconditional elimination rule.