Consider the following premises. forall x_11: P(x_11) <-> Q_11(x_11). forall x_11: P(x_11) <-> Q_11(x_11). Can we infer P(a_2) -> Q_11(a_2) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P(x_11) <-> Q_11(x_11) we can infer forall x_11: Q_11(x_11) -> P(x_11) via universal biconditional elimination. From forall x_11: P(x_11) <-> Q_11(x_11) we can infer forall x_11: P(x_11) -> Q_11(x_11) via universal biconditional elimination. From forall x_11: P(x_11) -> Q_11(x_11), forall x_11: Q_11(x_11) -> P(x_11) we can infer forall x_11: P(x_11) <-> Q_11(x_11) via universal biconditional introduction. From forall x_11: P(x_11) <-> Q_11(x_11) we can infer P(a_2) <-> Q_11(a_2) via universal instantiation. Finally, from P(a_2) <-> Q_11(a_2) we can infer P(a_2) -> Q_11(a_2) via biconditional elimination. Therefore, the answer is yes.