Consider the following premises. forall x_12: R_12(x_12) -> S_12(x_12). R_12(a_12) -> S_12(a_12). S_12(a_12) -> R_12(a_12). Can we infer R_12(a_12) <-> S_12(a_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: R_12(x_12) -> S_12(x_12) we can infer R_12(a_12) -> S_12(a_12) via universal instantiation. Finally, from R_12(a_12) -> S_12(a_12), S_12(a_12) -> R_12(a_12) we can infer R_12(a_12) <-> S_12(a_12) via biconditional introduction. Therefore, the answer is yes.