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, x is excited. For all x, if x were a nurse, then x is not excited. For all x, x is a nurse if and only if x will cook.
For all x, x is not a nurse can be inferred via the universal modus tollens rule. For all x, if x were a nurse, then x is cooking can be inferred via the universal biconditional elimination rule. For all x, if x cooks, then x is a nurse can be inferred via the universal biconditional elimination rule.