Consider the following premises. exists x: R_4(x) -> U_1(x). forall x: S_4(x) -> R_4(x). forall x: S_4(x) <-> U_1(x). Can we infer exists x: S_4(x) -> U_1(x) from them? If possible, name the inference rules being used at each step.
 From forall x: S_4(x) <-> U_1(x) we can infer forall x: U_1(x) -> S_4(x) via universal biconditional elimination. Finally, from forall x: S_4(x) -> R_4(x), exists x: R_4(x) -> U_1(x) we can infer exists x: S_4(x) -> U_1(x) via existential transitivity. Therefore, the answer is yes.