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