Consider the following premises. forall x_4: P_4(x_4) <-> Q_4(x_4). forall x_4: Q_4(x_4) -> P_4(x_4). Can we infer forall x_4: P_4(x_4) -> Q_4(x_4) from them? If possible, name the inference rules being used at each step.
We can infer forall x_4: P_4(x_4) -> Q_4(x_4) via the universal biconditional elimination rule. Therefore, the answer is yes.