Consider the following premises. forall x: S(x) <-> U_2(x). forall x: S(x) -> U_2(x). exists x: U_2(x) <-> S(x). Can we infer exists x: U_2(x) <-> S(x) from them? If possible, name the inference rules being used at each step.
That is one of the premises. Therefore, the answer is yes.