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: There is at least one x for which x will cook if and only if x is an office clerk. For all x, if x were rich, then x is cooking. For all x, x is not an office clerk. For all x, if x cooks, then x is rich.
For all x, x is rich if and only if x will cook can be inferred via the universal biconditional introduction rule. For all x, x will cook if and only if x is rich can be inferred via the universal biconditional introduction rule. There is at least one x for which if x cooks, then x is an office clerk can be inferred via the existential biconditional elimination rule. There is at least one x for which if x were an office clerk, then x is cooking can be inferred via the existential biconditional elimination rule. There is at least one x for which x will not cook can be inferred via the existential biconditional elimination rule.