Consider the following premises. forall x_4: R(x_4) -> T_4(x_4). forall x_4: T_1(x_4) <-> R(x_4). exists x_4: T_4(x_4) -> T_1(x_4). Can we infer exists x_4: R(x_4) <-> T_4(x_4) from them? If possible, name the inference rules being used at each step.
 From forall x_4: T_1(x_4) <-> R(x_4) we can infer forall x_4: T_1(x_4) -> R(x_4) via universal biconditional elimination. From exists x_4: T_4(x_4) -> T_1(x_4), forall x_4: T_1(x_4) -> R(x_4) we can infer exists x_4: T_4(x_4) -> R(x_4) via existential transitivity. Finally, from forall x_4: R(x_4) -> T_4(x_4), exists x_4: T_4(x_4) -> R(x_4) we can infer exists x_4: R(x_4) <-> T_4(x_4) via existential biconditional introduction. Therefore, the answer is yes.