Consider the following premises. forall x_4: Q(x_4) -> T(x_4). T(a_7) -> Q(a_7). forall x_4: Q(x_4) <-> T(x_4). Can we infer Q(a_7) <-> T(a_7) from them? If possible, name the inference rules being used at each step.
 From forall x_4: Q(x_4) <-> T(x_4) we can infer forall x_4: T(x_4) -> Q(x_4) via universal biconditional elimination. From forall x_4: Q(x_4) -> T(x_4), forall x_4: T(x_4) -> Q(x_4) we can infer forall x_4: Q(x_4) <-> T(x_4) via universal biconditional introduction. Finally, from forall x_4: Q(x_4) <-> T(x_4) we can infer Q(a_7) <-> T(a_7) via universal instantiation. Therefore, the answer is yes.