Consider the following premises. forall z_3: U_2(z_3). exists z_3: U_3(z_3). forall z_3: U_3(z_3) -> T_2(z_3). Can we infer exists z_3: U_2(z_3) from them?
 From forall z_3: U_3(z_3) -> T_2(z_3), exists z_3: U_3(z_3) we can infer exists z_3: T_2(z_3). From forall z_3: U_2(z_3), exists z_3: T_2(z_3) we can infer exists z_3: U_2(z_3) and T_2(z_3). Finally, from exists z_3: U_2(z_3) and T_2(z_3) we can infer exists z_3: U_2(z_3). Therefore, the answer is yes.