Consider the following premises. exists x: R_4(x) or ~W(x). forall x: R_4(x) <-> W(x). Can we infer exists x: W(x) -> R_4(x) from them? If possible, name the inference rules being used at each step.
 From forall x: R_4(x) <-> W(x) we can infer forall x: R_4(x) -> W(x) via universal biconditional elimination. Finally, from exists x: R_4(x) or ~W(x) we can infer exists x: W(x) -> R_4(x) via existential rewriting. Therefore, the answer is yes.