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 Joseph were a cashier, then David is writing a letter. It is not snowing. It is snowing if and only if James is a janitor. If David writes a letter, then James is a janitor. If it is late, then Joseph is a cashier.
If Joseph were a cashier, then James is a janitor can be inferred via the transitivity rule. If it is late, then David is writing a letter can be inferred via the transitivity rule. If it snows, then James is a janitor can be inferred via the biconditional elimination rule. If James were a janitor, then it is snowing can be inferred via the biconditional elimination rule. James is not a janitor can be inferred via the biconditional elimination rule.