Consider the following premises. forall x_12: P_6(x_12) -> P_12(x_12). Q_12(b) -> P_6(b). forall x_12: P_12(x_12) <-> Q_12(x_12). Can we infer P_6(b) <-> Q_12(b) from them? If possible, name the inference rules being used at each step.
 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) via universal biconditional elimination. 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) via universal transitivity. From forall x_12: P_6(x_12) -> Q_12(x_12) we can infer P_6(b) -> Q_12(b) via universal instantiation. Finally, from P_6(b) -> Q_12(b), Q_12(b) -> P_6(b) we can infer P_6(b) <-> Q_12(b) via biconditional introduction. Therefore, the answer is yes.