Consider the following premises. S_5(g_3) -> S(g_3). forall x_5: S(x_5) -> S_5(x_5). Can we infer S_5(g_3) <-> S(g_3) from them? If possible, name the inference rules being used at each step.
 From forall x_5: S(x_5) -> S_5(x_5) we can infer S(g_3) -> S_5(g_3) via universal instantiation. Finally, from S_5(g_3) -> S(g_3), S(g_3) -> S_5(g_3) we can infer S_5(g_3) <-> S(g_3) via biconditional introduction. Therefore, the answer is yes.