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: William is not cooking. If Elisabeth were sad, then William is cooking. For all z, z is sad if and only if z is a doctor.
Elisabeth is not sad can be inferred via the modus tollens rule. For all z, if z were sad, then z is a doctor can be inferred via the universal biconditional elimination rule. For all z, if z were a doctor, then z is sad can be inferred via the universal biconditional elimination rule.