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 x, if x were a writer, then x is a server. For all x, if x were a server, then x is climbing a mountain. For all x, x is not a writer. There is at least one x for which x is a cashier if and only if x will climb a mountain. For all x, x is a writer if and only if x will climb a mountain.
For all x, if x were a writer, then x is climbing a mountain can be inferred via the universal transitivity rule. For all x, if x were a writer, then x is climbing a mountain can be inferred via the universal biconditional elimination rule. There is at least one x for which if x were a cashier, then x is climbing a mountain can be inferred via the existential biconditional elimination rule. For all x, if x climbs a mountain, then x is a writer can be inferred via the universal biconditional elimination rule. There is at least one x for which if x climbs a mountain, then x is a cashier can be inferred via the existential biconditional elimination rule. For all x, x will not climb a mountain can be inferred via the universal biconditional elimination rule.