Consider the following premises. forall x: U_1(x) -> R_3(x). exists x: R_3(x) -> T(x). forall x: T(x) -> Q(x). forall x: Q(x) -> U_1(x). Can we infer exists x: Q(x) <-> U_1(x) from them? If possible, name the inference rules being used at each step.
 From forall x: U_1(x) -> R_3(x), exists x: R_3(x) -> T(x) we can infer exists x: U_1(x) -> T(x) via existential transitivity. From exists x: U_1(x) -> T(x), forall x: T(x) -> Q(x) we can infer exists x: U_1(x) -> Q(x) via existential transitivity. Finally, from forall x: Q(x) -> U_1(x), exists x: U_1(x) -> Q(x) we can infer exists x: Q(x) <-> U_1(x) via existential biconditional introduction. Therefore, the answer is yes.