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