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 x_4, x_4 will not cook. For all x_4, if x_4 were a carpenter, then x_4 is playing tennis. For all x_4, if x_4 plays tennis, then x_4 is a nurse. For all x_4, x_4 is a nurse if and only if x_4 will cook.
For all x_4, if x_4 were a carpenter, then x_4 is a nurse can be inferred via the universal transitivity rule. For all x_4, if x_4 were a nurse, then x_4 is cooking can be inferred via the universal biconditional elimination rule. For all x_4, if x_4 cooks, then x_4 is a nurse can be inferred via the universal biconditional elimination rule. For all x_4, x_4 is not a nurse can be inferred via the universal biconditional elimination rule.