Consider the following premises. Q_4(a) -> w_2. forall z_3: ~Q_4(z_3). w_2 -> Q_4(a). Can we infer ~w_2 from them? If possible, name the inference rules being used at each step.
 From forall z_3: ~Q_4(z_3) we can infer ~Q_4(a) via universal instantiation. From Q_4(a) -> w_2, w_2 -> Q_4(a) we can infer Q_4(a) <-> w_2 via biconditional introduction. Finally, from Q_4(a) <-> w_2, ~Q_4(a) we can infer ~w_2 via biconditional elimination. Therefore, the answer is yes.