Consider the following premises. forall x_8: P_8(x_8) <-> W_4(x_8). forall x_8: P_8(x_8) -> R_1(x_8). forall x_8: R_1(x_8) -> R(x_8). Can we infer forall x_8: W_4(x_8) -> R(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) <-> W_4(x_8) we can infer forall x_8: W_4(x_8) -> P_8(x_8) via universal biconditional elimination. From forall x_8: W_4(x_8) -> P_8(x_8), forall x_8: P_8(x_8) -> R_1(x_8) we can infer forall x_8: W_4(x_8) -> R_1(x_8) via universal transitivity. Finally, from forall x_8: W_4(x_8) -> R_1(x_8), forall x_8: R_1(x_8) -> R(x_8) we can infer forall x_8: W_4(x_8) -> R(x_8) via universal transitivity. Therefore, the answer is yes.