Consider the following premises. forall x_8: P_8(x_8) <-> Q_8(x_8). forall x_8: P_8(x_8). Can we infer exists x: Q_8(x) from them?
 From forall x_8: P_8(x_8) <-> Q_8(x_8) we can infer forall x_8: P_8(x_8) -> Q_8(x_8). From forall x_8: P_8(x_8) -> Q_8(x_8), forall x_8: P_8(x_8) we can infer forall x_8: Q_8(x_8). From forall x_8: Q_8(x_8) we can infer Q_8(a_1). Finally, from Q_8(a_1) we can infer exists x: Q_8(x). Therefore, the answer is yes.