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: For all z, if z were a cashier, then z is climbing a mountain. There is at least one z for which z is a cashier if and only if z is a lawyer. For all z, z will not climb a mountain. For all z, if z climbs a mountain, then z is a cashier.
For all z, z is not a cashier can be inferred via the universal modus tollens rule. For all z, z is a cashier if and only if z will climb a mountain can be inferred via the universal biconditional introduction rule. For all z, z will climb a mountain if and only if z is a cashier can be inferred via the universal biconditional introduction rule. There is at least one z for which if z were a cashier, then z is a lawyer can be inferred via the existential biconditional elimination rule. There is at least one z for which if z were a lawyer, then z is a cashier can be inferred via the existential biconditional elimination rule.