Consider the following premises. forall y: P(y) <-> U(y). forall y: T(y) -> P(y). exists y: U(y) -> S_1(y). Can we infer exists y: T(y) -> S_1(y) from them? If possible, name the inference rules being used at each step.
 From forall y: P(y) <-> U(y) we can infer forall y: P(y) -> U(y) via universal biconditional elimination. From forall y: T(y) -> P(y), forall y: P(y) -> U(y) we can infer forall y: T(y) -> U(y) via universal transitivity. Finally, from forall y: T(y) -> U(y), exists y: U(y) -> S_1(y) we can infer exists y: T(y) -> S_1(y) via existential transitivity. Therefore, the answer is yes.