Consider the following premises. Q(a_7) <-> w. forall x_8: Q_8(x_8) -> Q(x_8). ~Q_8(a_7). forall x_8: Q(x_8) -> Q_8(x_8). Can we infer w from them? If possible, name the inference rules being used at each step.
 From forall x_8: Q(x_8) -> Q_8(x_8), forall x_8: Q_8(x_8) -> Q(x_8) we can infer forall x_8: Q(x_8) <-> Q_8(x_8) via universal biconditional introduction. From forall x_8: Q(x_8) <-> Q_8(x_8) we can infer Q(a_7) <-> Q_8(a_7) via universal instantiation. From Q(a_7) <-> Q_8(a_7), ~Q_8(a_7) we can infer ~Q(a_7) via biconditional elimination. Finally, from Q(a_7) <-> w, ~Q(a_7) we can infer ~w via biconditional elimination, which contradicts w. Therefore, the answer is no.