Consider the following premises. forall y_2: U(y_2) <-> T(y_2). forall y_2: U(y_2) -> T(y_2). forall y_2: ~T(y_2). Can we infer forall y_2: ~U(y_2) from them?
 From forall y_2: U(y_2) <-> T(y_2) we can infer forall y_2: T(y_2) -> U(y_2). From forall y_2: T(y_2) -> U(y_2), forall y_2: U(y_2) -> T(y_2) we can infer forall y_2: T(y_2) <-> U(y_2). Finally, from forall y_2: T(y_2) <-> U(y_2), forall y_2: ~T(y_2) we can infer forall y_2: ~U(y_2). Therefore, the answer is yes.