Consider the following premises. forall x_9: P_9(x_9) and Q_9(x_9). forall x_9: Q_6(x_9). Can we infer exists x: P_9(x) from them?
 From forall x_9: P_9(x_9) and Q_9(x_9) we can infer forall x_9: P_9(x_9). From forall x_9: P_9(x_9), forall x_9: Q_6(x_9) we can infer forall x_9: P_9(x_9) and Q_6(x_9). From forall x_9: P_9(x_9) and Q_6(x_9) we can infer forall x_9: P_9(x_9). From forall x_9: P_9(x_9) we can infer P_9(j). Finally, from P_9(j) we can infer exists x: P_9(x). Therefore, the answer is yes.