Consider the following premises. forall y: P_3(y). forall y: U(y) <-> P_3(y). Can we infer forall y: U(y) from them?
 From forall y: U(y) <-> P_3(y) we can infer forall y: P_3(y) -> U(y). Finally, from forall y: P_3(y) -> U(y), forall y: P_3(y) we can infer forall y: U(y). Therefore, the answer is yes.