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_4, z_4 is a nurse if and only if z_4 will play tennis. Barbara is not a nurse. For all z_4, if z_4 plays tennis, then z_4 is a nurse.
For all z_4, if z_4 were a nurse, then z_4 is playing tennis can be inferred via the universal biconditional elimination rule. For all z_4, if z_4 plays tennis, then z_4 is a nurse can be inferred via the universal biconditional elimination rule.