Consider the following premises. forall y_1: S(y_1) -> P_4(y_1). forall y_1: P_4(y_1) -> S(y_1). Can we infer forall y_1: S(y_1) <-> P_4(y_1) from them? If possible, name the inference rules being used at each step.
We can infer forall y_1: S(y_1) <-> P_4(y_1) via the universal biconditional introduction rule. Therefore, the answer is yes.