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 z, z is a nurse if and only if z will work. For all z, z will not work. There is at least one z for which z will play tennis if and only if z is a nurse.
For all z, if z were a nurse, then z is working can be inferred via the universal biconditional elimination rule. There is at least one z for which if z plays tennis, then z is a nurse can be inferred via the existential biconditional elimination rule. For all z, if z works, then z is a nurse can be inferred via the universal biconditional elimination rule. There is at least one z for which if z were a nurse, then z is playing tennis can be inferred via the existential biconditional elimination rule. For all z, z is not a nurse can be inferred via the universal biconditional elimination rule.