Consider the following premises. forall x_12: P_12(x_12) <-> Q_12(x_12). Q_12(b) -> P_6(b). forall x_12: P_6(x_12) -> P_12(x_12). Can we infer P_6(b) <-> Q_12(b) from them?
 From forall x_12: P_12(x_12) <-> Q_12(x_12) we can infer forall x_12: P_12(x_12) -> Q_12(x_12). From forall x_12: P_6(x_12) -> P_12(x_12), forall x_12: P_12(x_12) -> Q_12(x_12) we can infer forall x_12: P_6(x_12) -> Q_12(x_12). From forall x_12: P_6(x_12) -> Q_12(x_12) we can infer P_6(b) -> Q_12(b). Finally, from P_6(b) -> Q_12(b), Q_12(b) -> P_6(b) we can infer P_6(b) <-> Q_12(b). Therefore, the answer is yes.