Consider the following premises. forall y: U_3(y) or ~U_4(y). forall y: U_3(y) <-> U_4(y). Can we infer exists y: ~(U_4(y) <-> U_3(y)) from them?
 From forall y: U_3(y) <-> U_4(y) we can infer forall y: U_3(y) -> U_4(y). From forall y: U_3(y) or ~U_4(y) we can infer forall y: U_4(y) -> U_3(y). Finally, from forall y: U_4(y) -> U_3(y), forall y: U_3(y) -> U_4(y) we can infer forall y: U_4(y) <-> U_3(y), which contradicts exists y: ~(U_4(y) <-> U_3(y)). Therefore, the answer is no.