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 were a nurse, then y_2 is happy. For all y_2, y_2 is happy if and only if y_2 is a nurse. For all y_2, y_2 is not a nurse. For all y_2, y_2 will take a plane if and only if y_2 is happy.
For all y_2, if y_2 were happy, then y_2 is a nurse can be inferred via the universal biconditional elimination rule. For all y_2, if y_2 takes a plane, then y_2 is happy can be inferred via the universal biconditional elimination rule. For all y_2, if y_2 were a nurse, then y_2 is happy can be inferred via the universal biconditional elimination rule. For all y_2, if y_2 were happy, then y_2 is taking a plane can be inferred via the universal biconditional elimination rule. For all y_2, y_2 is not happy can be inferred via the universal biconditional elimination rule.