Consider the following premises. forall y: T(y) -> Q_2(y). forall y: T_3(y) -> Q_2(y). exists y: Q_2(y) -> T(y). forall y: ~T(y). Can we infer exists y: ~T_3(y) from them? If possible, name the inference rules being used at each step.
 From exists y: Q_2(y) -> T(y), forall y: T(y) -> Q_2(y) we can infer exists y: Q_2(y) <-> T(y) via existential biconditional introduction. From exists y: Q_2(y) <-> T(y), forall y: ~T(y) we can infer exists y: ~Q_2(y) via existential biconditional elimination. Finally, from forall y: T_3(y) -> Q_2(y), exists y: ~Q_2(y) we can infer exists y: ~T_3(y) via existential modus tollens. Therefore, the answer is yes.