Consider the following premises. forall x_7: P_7(x_7) or ~Q_7(x_7). P_7(g_4) -> Q_7(g_4). Can we infer Q_7(g_4) <-> P_7(g_4) from them?
 From forall x_7: P_7(x_7) or ~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(g_4) -> P_7(g_4). Finally, from Q_7(g_4) -> P_7(g_4), P_7(g_4) -> Q_7(g_4) we can infer Q_7(g_4) <-> P_7(g_4). Therefore, the answer is yes.