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 janitor if and only if Joseph is a scientist. If Richard were happy, then Joseph is a scientist. If Elisabeth were a janitor, then Richard is happy.
If Elisabeth were a janitor, then Joseph is a scientist can be inferred via the transitivity rule. If Elisabeth were a janitor, then Joseph is a scientist can be inferred via the biconditional elimination rule. If Joseph were a scientist, then Elisabeth is a janitor can be inferred via the biconditional elimination rule.