Consider the following premises. exists y: T(y) or ~Q(y). forall y: Q(y) or ~T(y). Can we infer exists y: T(y) -> Q(y) from them? If possible, name the inference rules being used at each step.
 From exists y: T(y) or ~Q(y) we can infer exists y: Q(y) -> T(y) via existential rewriting. From forall y: Q(y) or ~T(y) we can infer forall y: T(y) -> Q(y) via universal rewriting. From exists y: Q(y) -> T(y), forall y: T(y) -> Q(y) we can infer exists y: Q(y) <-> T(y) via existential biconditional introduction. Finally, from exists y: Q(y) <-> T(y) we can infer exists y: T(y) -> Q(y) via existential biconditional elimination. Therefore, the answer is yes.