Consider the following premises. forall y_3: W(y_3) -> Q_3(y_3). forall y_3: T_4(y_3) -> Q_3(y_3). exists y_3: Q_3(y_3) -> T_4(y_3). forall y_3: Q_3(y_3) -> W(y_3). Can we infer exists y_3: T_4(y_3) -> W(y_3) from them? If possible, name the inference rules being used at each step.
 From forall y_3: Q_3(y_3) -> W(y_3), forall y_3: W(y_3) -> Q_3(y_3) we can infer forall y_3: Q_3(y_3) <-> W(y_3) via universal biconditional introduction. From forall y_3: Q_3(y_3) <-> W(y_3) we can infer forall y_3: Q_3(y_3) -> W(y_3) via universal biconditional elimination. From forall y_3: T_4(y_3) -> Q_3(y_3), exists y_3: Q_3(y_3) -> T_4(y_3) we can infer exists y_3: T_4(y_3) <-> Q_3(y_3) via existential biconditional introduction. From exists y_3: T_4(y_3) <-> Q_3(y_3) we can infer exists y_3: T_4(y_3) -> Q_3(y_3) via existential biconditional elimination. Finally, from exists y_3: T_4(y_3) -> Q_3(y_3), forall y_3: Q_3(y_3) -> W(y_3) we can infer exists y_3: T_4(y_3) -> W(y_3) via existential transitivity. Therefore, the answer is yes.