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 Richard listens to a song, then it is snowing. If Joseph were a cashier, then it is sunny. If it is sunny, then Richard is listening to a song. Joseph is a cashier if and only if it is snowing.
If Joseph were a cashier, then Richard is listening to a song can be inferred via the transitivity rule. If it is sunny, then it is snowing can be inferred via the transitivity rule. If Joseph were a cashier, then it is snowing can be inferred via the biconditional elimination rule. If it snows, then Joseph is a cashier can be inferred via the biconditional elimination rule.