Consider the following premises. forall x: S(x) <-> Q_2(x). forall x: S(x) -> R_3(x). exists x: R(x) -> Q_2(x). Can we infer exists x: R(x) -> R_3(x) from them? If possible, name the inference rules being used at each step.
 From forall x: S(x) <-> Q_2(x) we can infer forall x: Q_2(x) -> S(x) via universal biconditional elimination. From forall x: Q_2(x) -> S(x), forall x: S(x) -> R_3(x) we can infer forall x: Q_2(x) -> R_3(x) via universal transitivity. Finally, from exists x: R(x) -> Q_2(x), forall x: Q_2(x) -> R_3(x) we can infer exists x: R(x) -> R_3(x) via existential transitivity. Therefore, the answer is yes.