Consider the following premises. exists y_4: T_4(y_4) <-> T(y_4). forall y_4: T_4(y_4) -> R_3(y_4). forall y_4: R_3(y_4) -> T_4(y_4). Can we infer exists y_4: T(y_4) -> R_3(y_4) from them? If possible, name the inference rules being used at each step.
 From exists y_4: T_4(y_4) <-> T(y_4) we can infer exists y_4: T(y_4) -> T_4(y_4) via existential biconditional elimination. From forall y_4: T_4(y_4) -> R_3(y_4), forall y_4: R_3(y_4) -> T_4(y_4) we can infer forall y_4: T_4(y_4) <-> R_3(y_4) via universal biconditional introduction. From forall y_4: T_4(y_4) <-> R_3(y_4) we can infer forall y_4: T_4(y_4) -> R_3(y_4) via universal biconditional elimination. Finally, from exists y_4: T(y_4) -> T_4(y_4), forall y_4: T_4(y_4) -> R_3(y_4) we can infer exists y_4: T(y_4) -> R_3(y_4) via existential transitivity. Therefore, the answer is yes.