Consider the following premises. exists x_15: W_4(x_15) <-> R(x_15). forall x_15: P_15(x_15) <-> W_4(x_15). forall x_15: P_15(x_15) -> R(x_15). Can we infer exists x_15: W_4(x_15) -> R(x_15) from them? If possible, name the inference rules being used at each step.
 From forall x_15: P_15(x_15) <-> W_4(x_15) we can infer forall x_15: W_4(x_15) -> P_15(x_15) via universal biconditional elimination. From forall x_15: W_4(x_15) -> P_15(x_15), forall x_15: P_15(x_15) -> R(x_15) we can infer forall x_15: W_4(x_15) -> R(x_15) via universal transitivity. From exists x_15: W_4(x_15) <-> R(x_15) we can infer exists x_15: R(x_15) -> W_4(x_15) via existential biconditional elimination. From forall x_15: W_4(x_15) -> R(x_15), exists x_15: R(x_15) -> W_4(x_15) we can infer exists x_15: W_4(x_15) <-> R(x_15) via existential biconditional introduction. Finally, from exists x_15: W_4(x_15) <-> R(x_15) we can infer exists x_15: W_4(x_15) -> R(x_15) via existential biconditional elimination. Therefore, the answer is yes.