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 y_2, if y_2 cooks, then y_2 is sleeping. For all y_2, if y_2 were rich, then y_2 is cooking. For all y_2, y_2 will sleep if and only if y_2 is rich.
For all y_2, if y_2 were rich, then y_2 is sleeping can be inferred via the universal transitivity rule. For all y_2, if y_2 sleeps, then y_2 is rich can be inferred via the universal biconditional elimination rule. For all y_2, if y_2 were rich, then y_2 is sleeping can be inferred via the universal biconditional elimination rule.