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