Consider the following premises. forall x_7: P_7(x_7) <-> Q_7(x_7). forall x_7: P_7(x_7) -> Q_7(x_7). Can we infer P_7(a_2) -> Q_7(a_2) from them?
 From forall x_7: P_7(x_7) <-> Q_7(x_7) we can infer forall x_7: Q_7(x_7) -> P_7(x_7). From forall x_7: Q_7(x_7) -> P_7(x_7), forall x_7: P_7(x_7) -> Q_7(x_7) we can infer forall x_7: Q_7(x_7) <-> P_7(x_7). From forall x_7: Q_7(x_7) <-> P_7(x_7) we can infer Q_7(a_2) <-> P_7(a_2). Finally, from Q_7(a_2) <-> P_7(a_2) we can infer P_7(a_2) -> Q_7(a_2). Therefore, the answer is yes.