Consider the following premises. forall x_9: T(x_9) -> Q_9(x_9). forall x_9: T(x_9) or ~Q_9(x_9). forall x_9: Q_9(x_9) -> T(x_9). Can we infer forall x_9: T(x_9) <-> Q_9(x_9) from them? If possible, name the inference rules being used at each step.
We can infer forall x_9: T(x_9) <-> Q_9(x_9) via the universal biconditional introduction rule. Therefore, the answer is yes.