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