Consider the following premises. exists y: W_1(y) <-> U(y). forall y: U(y) -> W_1(y). Can we infer exists y: U(y) <-> W_1(y) from them? If possible, name the inference rules being used at each step.
 From exists y: W_1(y) <-> U(y) we can infer exists y: W_1(y) -> U(y) via existential biconditional elimination. Finally, from forall y: U(y) -> W_1(y), exists y: W_1(y) -> U(y) we can infer exists y: U(y) <-> W_1(y) via existential biconditional introduction. Therefore, the answer is yes.