Consider the following premises. forall y: Q_4(y) -> R(y). forall y: R(y) -> Q_4(y). exists y: Q_4(y) <-> W(y). forall y: ~W(y). Can we infer exists y: ~R(y) from them? If possible, name the inference rules being used at each step.
 From exists y: Q_4(y) <-> W(y), forall y: ~W(y) we can infer exists y: ~Q_4(y) via existential biconditional elimination. From forall y: Q_4(y) -> R(y), forall y: R(y) -> Q_4(y) we can infer forall y: Q_4(y) <-> R(y) via universal biconditional introduction. Finally, from forall y: Q_4(y) <-> R(y), exists y: ~Q_4(y) we can infer exists y: ~R(y) via existential biconditional elimination. Therefore, the answer is yes.