Consider the following premises. forall x_1: P_2(x_1) <-> R(x_1). forall x_1: R(x_1) -> P_2(x_1). forall x_1: P_2(x_1) -> R(x_1). Can we infer forall x_1: R(x_1) <-> P_2(x_1) from them? If possible, name the inference rules being used at each step.
We can infer forall x_1: R(x_1) <-> P_2(x_1) via the universal biconditional introduction rule. Therefore, the answer is yes.