Consider the following premises. forall y: P_3(y) <-> S_2(y). r_6 <-> S_2(e). P_3(e) -> r_6. Can we infer S_2(e) <-> r_6 from them?
 From forall y: P_3(y) <-> S_2(y) we can infer forall y: S_2(y) -> P_3(y). From forall y: S_2(y) -> P_3(y) we can infer S_2(e) -> P_3(e). From S_2(e) -> P_3(e), P_3(e) -> r_6 we can infer S_2(e) -> r_6. From r_6 <-> S_2(e) we can infer r_6 -> S_2(e). Finally, from S_2(e) -> r_6, r_6 -> S_2(e) we can infer S_2(e) <-> r_6. Therefore, the answer is yes.