Consider the following premises. forall z_2: Q_4(z_2) -> W(z_2). exists z_2: W(z_2) -> Q_4(z_2). forall z_2: U(z_2) -> W(z_2). Can we infer exists z_2: U(z_2) -> Q_4(z_2) from them?
 From exists z_2: W(z_2) -> Q_4(z_2), forall z_2: Q_4(z_2) -> W(z_2) we can infer exists z_2: W(z_2) <-> Q_4(z_2). From exists z_2: W(z_2) <-> Q_4(z_2) we can infer exists z_2: W(z_2) -> Q_4(z_2). Finally, from forall z_2: U(z_2) -> W(z_2), exists z_2: W(z_2) -> Q_4(z_2) we can infer exists z_2: U(z_2) -> Q_4(z_2). Therefore, the answer is yes.