Consider the following premises. forall y_2: W_1(y_2) or ~R_1(y_2). exists y_2: W_1(y_2) -> R_1(y_2). Can we infer exists y_2: R_1(y_2) -> W_1(y_2) from them? If possible, name the inference rules being used at each step.
 From forall y_2: W_1(y_2) or ~R_1(y_2) we can infer forall y_2: R_1(y_2) -> W_1(y_2) via universal rewriting. From forall y_2: R_1(y_2) -> W_1(y_2), exists y_2: W_1(y_2) -> R_1(y_2) we can infer exists y_2: R_1(y_2) <-> W_1(y_2) via existential biconditional introduction. Finally, from exists y_2: R_1(y_2) <-> W_1(y_2) we can infer exists y_2: R_1(y_2) -> W_1(y_2) via existential biconditional elimination. Therefore, the answer is yes.