Consider the following premises. forall z: Q_3(z). forall z: T(z) <-> P_4(z). forall z: T(z) -> ~Q_3(z). Can we infer forall z: ~P_4(z) from them? If possible, name the inference rules being used at each step.
 From forall z: T(z) -> ~Q_3(z), forall z: Q_3(z) we can infer forall z: ~T(z) via universal modus tollens. Finally, from forall z: T(z) <-> P_4(z), forall z: ~T(z) we can infer forall z: ~P_4(z) via universal biconditional elimination. Therefore, the answer is yes.