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: Elisabeth is a nurse if and only if Joseph is sleeping. For all x_10, x_10 will not sleep. If it is cold, then Elisabeth is a nurse.
If Elisabeth were a nurse, then Joseph is sleeping can be inferred via the biconditional elimination rule. If Joseph sleeps, then Elisabeth is a nurse can be inferred via the biconditional elimination rule.