Consider the following premises. exists z: U(z) <-> U_3(z). forall z: Q_1(z) <-> U(z). Can we infer exists z: U_3(z) -> Q_1(z) from them? If possible, name the inference rules being used at each step.
 From forall z: Q_1(z) <-> U(z) we can infer forall z: U(z) -> Q_1(z) via universal biconditional elimination. From exists z: U(z) <-> U_3(z) we can infer exists z: U_3(z) -> U(z) via existential biconditional elimination. Finally, from exists z: U_3(z) -> U(z), forall z: U(z) -> Q_1(z) we can infer exists z: U_3(z) -> Q_1(z) via existential transitivity. Therefore, the answer is yes.