Consider the following premises. P_3(e_4). forall x_9: P_9(x_9) <-> P_3(x_9). Can we infer P_9(e_4) from them?
 From forall x_9: P_9(x_9) <-> P_3(x_9) we can infer forall x_9: P_3(x_9) -> P_9(x_9). From forall x_9: P_3(x_9) -> P_9(x_9) we can infer P_3(e_4) -> P_9(e_4). Finally, from P_3(e_4) -> P_9(e_4), P_3(e_4) we can infer P_9(e_4). Therefore, the answer is yes.