Consider the following premises. exists x_3: P_3(x_3) or ~R(x_3). forall x_3: P_3(x_3) -> R(x_3). Can we infer exists x_3: R(x_3) <-> P_3(x_3) from them? If possible, name the inference rules being used at each step.
 From exists x_3: P_3(x_3) or ~R(x_3) we can infer exists x_3: R(x_3) -> P_3(x_3) via existential rewriting. Finally, from exists x_3: R(x_3) -> P_3(x_3), forall x_3: P_3(x_3) -> R(x_3) we can infer exists x_3: R(x_3) <-> P_3(x_3) via existential biconditional introduction. Therefore, the answer is yes.