Consider the following premises. forall x_8: Q_8(x_8) -> R_8(x_8). forall x_8: P_3(x_8) -> Q_8(x_8). forall x_8: P_3(x_8) or ~R_8(x_8). Can we infer P_3(h) -> R_8(h) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_3(x_8) -> Q_8(x_8), forall x_8: Q_8(x_8) -> R_8(x_8) we can infer forall x_8: P_3(x_8) -> R_8(x_8) via universal transitivity. From forall x_8: P_3(x_8) or ~R_8(x_8) we can infer forall x_8: R_8(x_8) -> P_3(x_8) via universal rewriting. From forall x_8: P_3(x_8) -> R_8(x_8), forall x_8: R_8(x_8) -> P_3(x_8) we can infer forall x_8: P_3(x_8) <-> R_8(x_8) via universal biconditional introduction. From forall x_8: P_3(x_8) <-> R_8(x_8) we can infer P_3(h) <-> R_8(h) via universal instantiation. Finally, from P_3(h) <-> R_8(h) we can infer P_3(h) -> R_8(h) via biconditional elimination. Therefore, the answer is yes.