Consider the following premises. forall y_2: T(y_2) -> P_3(y_2). exists y_2: P_3(y_2) -> P(y_2). forall y_2: W(y_2) -> T(y_2). forall y_2: R(y_2) <-> W(y_2). Can we infer exists y_2: R(y_2) -> P(y_2) from them? If possible, name the inference rules being used at each step.
 From forall y_2: R(y_2) <-> W(y_2) we can infer forall y_2: R(y_2) -> W(y_2) via universal biconditional elimination. From forall y_2: W(y_2) -> T(y_2), forall y_2: T(y_2) -> P_3(y_2) we can infer forall y_2: W(y_2) -> P_3(y_2) via universal transitivity. From forall y_2: W(y_2) -> P_3(y_2), exists y_2: P_3(y_2) -> P(y_2) we can infer exists y_2: W(y_2) -> P(y_2) via existential transitivity. Finally, from forall y_2: R(y_2) -> W(y_2), exists y_2: W(y_2) -> P(y_2) we can infer exists y_2: R(y_2) -> P(y_2) via existential transitivity. Therefore, the answer is yes.