Consider the following premises. exists x_8: P_5(x_8) <-> P(x_8). forall x_8: R_2(x_8) <-> P(x_8). Can we infer exists x_8: R_2(x_8) -> P_5(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: R_2(x_8) <-> P(x_8) we can infer forall x_8: R_2(x_8) -> P(x_8) via universal biconditional elimination. From exists x_8: P_5(x_8) <-> P(x_8) we can infer exists x_8: P(x_8) -> P_5(x_8) via existential biconditional elimination. Finally, from forall x_8: R_2(x_8) -> P(x_8), exists x_8: P(x_8) -> P_5(x_8) we can infer exists x_8: R_2(x_8) -> P_5(x_8) via existential transitivity. Therefore, the answer is yes.