Consider the following premises. exists x: U_3(x) -> R(x). forall x: Q_2(x) -> U_3(x). forall x: R(x) -> Q_2(x). Can we infer exists x: R(x) -> Q_2(x) from them? If possible, name the inference rules being used at each step.
 From forall x: Q_2(x) -> U_3(x), exists x: U_3(x) -> R(x) we can infer exists x: Q_2(x) -> R(x) via existential transitivity. From forall x: R(x) -> Q_2(x), exists x: Q_2(x) -> R(x) we can infer exists x: R(x) <-> Q_2(x) via existential biconditional introduction. Finally, from exists x: R(x) <-> Q_2(x) we can infer exists x: R(x) -> Q_2(x) via existential biconditional elimination. Therefore, the answer is yes.