Consider the following premises. forall y: T(y) -> S(y). exists y: S(y) <-> U_1(y). Can we infer exists y: T(y) -> U_1(y) from them? If possible, name the inference rules being used at each step.
 From exists y: S(y) <-> U_1(y) we can infer exists y: S(y) -> U_1(y) via existential biconditional elimination. Finally, from forall y: T(y) -> S(y), exists y: S(y) -> U_1(y) we can infer exists y: T(y) -> U_1(y) via existential transitivity. Therefore, the answer is yes.