Consider the following premises. forall x_13: P_13(x_13) and Q_13(x_13). forall x: Q(x). Can we infer exists x: Q(x) and P_13(x) from them?
 From forall x_13: P_13(x_13) and Q_13(x_13) we can infer forall x_13: P_13(x_13). From forall x_13: P_13(x_13) we can infer P_13(a_10). From P_13(a_10) we can infer exists x: P_13(x). Finally, from forall x: Q(x), exists x: P_13(x) we can infer exists x: Q(x) and P_13(x). Therefore, the answer is yes.