Consider the following premises. Q_4(a) -> W_3(a). forall z: W_3(z) -> R_4(z). forall z: R_4(z) -> Q_4(z). Can we infer W_3(a) <-> Q_4(a) from them?
 From forall z: W_3(z) -> R_4(z), forall z: R_4(z) -> Q_4(z) we can infer forall z: W_3(z) -> Q_4(z). From forall z: W_3(z) -> Q_4(z) we can infer W_3(a) -> Q_4(a). Finally, from W_3(a) -> Q_4(a), Q_4(a) -> W_3(a) we can infer W_3(a) <-> Q_4(a). Therefore, the answer is yes.