Consider the following premises. forall x_10: P_10(x_10). forall x: P_10(x) -> U_3(x). Can we infer exists x: U_3(x) from them?
 From forall x_10: P_10(x_10) we can infer P_10(f_1). From P_10(f_1) we can infer exists x: P_10(x). Finally, from forall x: P_10(x) -> U_3(x), exists x: P_10(x) we can infer exists x: U_3(x). Therefore, the answer is yes.