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