Consider the following premises. P_8(a_5). forall x_8: P_8(x_8) <-> Q_8(x_8). Can we infer ~Q_8(a_5) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) <-> Q_8(x_8) we can infer forall x_8: P_8(x_8) -> Q_8(x_8) via universal biconditional elimination. From forall x_8: P_8(x_8) -> Q_8(x_8) we can infer P_8(a_5) -> Q_8(a_5) via universal instantiation. Finally, from P_8(a_5) -> Q_8(a_5), P_8(a_5) we can infer Q_8(a_5) via modus ponens, which contradicts ~Q_8(a_5). Therefore, the answer is no.