Consider the following premises. forall y: Q_3(y) -> U(y). exists y: U(y) <-> Q_3(y). Can we infer exists y: Q_3(y) -> U(y) from them? If possible, name the inference rules being used at each step.
 From exists y: U(y) <-> Q_3(y) we can infer exists y: U(y) -> Q_3(y) via existential biconditional elimination. From forall y: Q_3(y) -> U(y), exists y: U(y) -> Q_3(y) we can infer exists y: Q_3(y) <-> U(y) via existential biconditional introduction. Finally, from exists y: Q_3(y) <-> U(y) we can infer exists y: Q_3(y) -> U(y) via existential biconditional elimination. Therefore, the answer is yes.