Consider the following premises. forall x_10: Q_1(x_10) -> P_10(x_10). forall x_10: Q_10(x_10) -> Q_1(x_10). forall x_10: P_10(x_10) <-> Q_10(x_10). Can we infer Q_1(a_2) -> Q_10(a_2) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) <-> Q_10(x_10) we can infer forall x_10: P_10(x_10) -> Q_10(x_10) via universal biconditional elimination. From forall x_10: Q_1(x_10) -> P_10(x_10), forall x_10: P_10(x_10) -> Q_10(x_10) we can infer forall x_10: Q_1(x_10) -> Q_10(x_10) via universal transitivity. From forall x_10: Q_1(x_10) -> Q_10(x_10), forall x_10: Q_10(x_10) -> Q_1(x_10) we can infer forall x_10: Q_1(x_10) <-> Q_10(x_10) via universal biconditional introduction. From forall x_10: Q_1(x_10) <-> Q_10(x_10) we can infer Q_1(a_2) <-> Q_10(a_2) via universal instantiation. Finally, from Q_1(a_2) <-> Q_10(a_2) we can infer Q_1(a_2) -> Q_10(a_2) via biconditional elimination. Therefore, the answer is yes.