Consider the following premises. exists y: T_1(y) <-> P_3(y). forall y: P_3(y) -> W(y). Can we infer exists y: T_1(y) -> W(y) from them? If possible, name the inference rules being used at each step.
 From exists y: T_1(y) <-> P_3(y) we can infer exists y: T_1(y) -> P_3(y) via existential biconditional elimination. Finally, from exists y: T_1(y) -> P_3(y), forall y: P_3(y) -> W(y) we can infer exists y: T_1(y) -> W(y) via existential transitivity. Therefore, the answer is yes.