Consider the following premises. forall x_8: P_8(x_8). forall x_7: P_8(x_7) <-> S_7(x_7). Can we infer S_7(a_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) we can infer P_8(a_8) via universal instantiation. From forall x_7: P_8(x_7) <-> S_7(x_7) we can infer P_8(a_8) <-> S_7(a_8) via universal instantiation. From P_8(a_8) <-> S_7(a_8) we can infer P_8(a_8) -> S_7(a_8) via biconditional elimination. Finally, from P_8(a_8) -> S_7(a_8), P_8(a_8) we can infer S_7(a_8) via modus ponens. Therefore, the answer is yes.