Consider the following premises. forall z: W(z) -> P_1(z). forall z: P_1(z) -> W(z). ~W(a). Can we infer ~P_1(a) from them?
 From forall z: P_1(z) -> W(z), forall z: W(z) -> P_1(z) we can infer forall z: P_1(z) <-> W(z). From forall z: P_1(z) <-> W(z) we can infer P_1(a) <-> W(a). Finally, from P_1(a) <-> W(a), ~W(a) we can infer ~P_1(a). Therefore, the answer is yes.