Consider the following premises. forall x_3: T_1(x_3). forall x_3: W(x_3) <-> T_2(x_3). exists x_3: W(x_3) -> ~T_1(x_3). Can we infer exists x_3: ~T_2(x_3) from them? If possible, name the inference rules being used at each step.
 From exists x_3: W(x_3) -> ~T_1(x_3), forall x_3: T_1(x_3) we can infer exists x_3: ~W(x_3) via existential modus tollens. Finally, from forall x_3: W(x_3) <-> T_2(x_3), exists x_3: ~W(x_3) we can infer exists x_3: ~T_2(x_3) via existential biconditional elimination. Therefore, the answer is yes.