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: John is a nurse if and only if John is sleeping. For all z_4, z_4 is a nurse if and only if z_4 will sleep.
If John were a nurse, then John is sleeping can be inferred via the biconditional elimination rule. If John sleeps, then John is a nurse can be inferred via the biconditional elimination rule. For all z_4, if z_4 were a nurse, then z_4 is sleeping can be inferred via the universal biconditional elimination rule. For all z_4, if z_4 sleeps, then z_4 is a nurse can be inferred via the universal biconditional elimination rule.