Consider the following premises. forall y: T(y) -> Q(y). exists y: T(y) <-> Q(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) <-> Q(y) we can infer exists y: Q(y) -> T(y) via existential biconditional elimination. From forall y: T(y) -> Q(y), exists y: Q(y) -> T(y) we can infer exists y: T(y) <-> Q(y) via existential biconditional introduction. Finally, from exists y: T(y) <-> Q(y) we can infer exists y: T(y) -> Q(y) via existential biconditional elimination. Therefore, the answer is yes.