Consider the following premises. forall y_1: U(y_1) or ~U_1(y_1). exists y_1: U(y_1) -> U_1(y_1). Can we infer exists y_1: U_1(y_1) <-> U(y_1) from them? If possible, name the inference rules being used at each step.
 From forall y_1: U(y_1) or ~U_1(y_1) we can infer forall y_1: U_1(y_1) -> U(y_1) via universal rewriting. Finally, from forall y_1: U_1(y_1) -> U(y_1), exists y_1: U(y_1) -> U_1(y_1) we can infer exists y_1: U_1(y_1) <-> U(y_1) via existential biconditional introduction. Therefore, the answer is yes.