Consider the following premises. forall x_3: T_1(x_3) -> W(x_3). exists x_3: W(x_3) -> S_4(x_3). forall x_3: Q_4(x_3) <-> T_1(x_3). Can we infer exists x_3: Q_4(x_3) -> S_4(x_3) from them? If possible, name the inference rules being used at each step.
 From forall x_3: T_1(x_3) -> W(x_3), exists x_3: W(x_3) -> S_4(x_3) we can infer exists x_3: T_1(x_3) -> S_4(x_3) via existential transitivity. From forall x_3: Q_4(x_3) <-> T_1(x_3) we can infer forall x_3: Q_4(x_3) -> T_1(x_3) via universal biconditional elimination. Finally, from forall x_3: Q_4(x_3) -> T_1(x_3), exists x_3: T_1(x_3) -> S_4(x_3) we can infer exists x_3: Q_4(x_3) -> S_4(x_3) via existential transitivity. Therefore, the answer is yes.