Consider the following premises. w_1 <-> w_2. forall x: Q_1(x). w_1 -> ~Q_1(a). Can we infer w_2 from them? If possible, name the inference rules being used at each step.
 From forall x: Q_1(x) we can infer Q_1(a) via universal instantiation. From w_1 -> ~Q_1(a), Q_1(a) we can infer ~w_1 via modus tollens. Finally, from w_1 <-> w_2, ~w_1 we can infer ~w_2 via biconditional elimination, which contradicts w_2. Therefore, the answer is no.