Consider the following premises. forall x: W(x) <-> U_2(x). forall x: U_2(x) or ~R(x). forall x: W(x) -> R(x). Can we infer forall x: U_2(x) <-> R(x) from them? If possible, name the inference rules being used at each step.
 From forall x: W(x) <-> U_2(x) we can infer forall x: U_2(x) -> W(x) via universal biconditional elimination. From forall x: U_2(x) or ~R(x) we can infer forall x: R(x) -> U_2(x) via universal rewriting. From forall x: U_2(x) -> W(x), forall x: W(x) -> R(x) we can infer forall x: U_2(x) -> R(x) via universal transitivity. Finally, from forall x: U_2(x) -> R(x), forall x: R(x) -> U_2(x) we can infer forall x: U_2(x) <-> R(x) via universal biconditional introduction. Therefore, the answer is yes.