Consider the following premises. ~p_3. forall z: P_2(z) <-> Q(z). p_3 <-> Q(g). Can we infer ~P_2(g) from them? If possible, name the inference rules being used at each step.
 From forall z: P_2(z) <-> Q(z) we can infer P_2(g) <-> Q(g) via universal instantiation. From p_3 <-> Q(g), ~p_3 we can infer ~Q(g) via biconditional elimination. Finally, from P_2(g) <-> Q(g), ~Q(g) we can infer ~P_2(g) via biconditional elimination. Therefore, the answer is yes.