Consider the following premises. forall x_13: P_3(x_13). forall x_13: P_3(x_13) -> P_11(x_13). forall x_13: Q_11(x_13) <-> Q(x_13). forall x_13: P_11(x_13) <-> Q_11(x_13). Can we infer forall x_13: Q_11(x_13) from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_3(x_13) we can infer forall x_13: P_3(x_13) or Q(x_13) via universal addition. From forall x_13: P_11(x_13) <-> Q_11(x_13) we can infer forall x_13: P_11(x_13) -> Q_11(x_13) via universal biconditional elimination. From forall x_13: P_3(x_13) -> P_11(x_13), forall x_13: P_11(x_13) -> Q_11(x_13) we can infer forall x_13: P_3(x_13) -> Q_11(x_13) via universal transitivity. From forall x_13: Q_11(x_13) <-> Q(x_13) we can infer forall x_13: Q(x_13) -> Q_11(x_13) via universal biconditional elimination. Finally, from forall x_13: P_3(x_13) -> Q_11(x_13), forall x_13: Q(x_13) -> Q_11(x_13), forall x_13: P_3(x_13) or Q(x_13) we can infer forall x_13: Q_11(x_13) via universal disjunction elimination. Therefore, the answer is yes.