Consider the following premises. forall y: Q_4(y) or ~Q(y). forall y: Q(y) or Q_1(y). forall y: Q_4(y) <-> Q_1(y). Can we infer forall y: Q_4(y) from them? If possible, name the inference rules being used at each step.
 From forall y: Q_4(y) <-> Q_1(y) we can infer forall y: Q_1(y) -> Q_4(y) via universal biconditional elimination. From forall y: Q_4(y) or ~Q(y) we can infer forall y: Q(y) -> Q_4(y) via universal rewriting. Finally, from forall y: Q(y) -> Q_4(y), forall y: Q_1(y) -> Q_4(y), forall y: Q(y) or Q_1(y) we can infer forall y: Q_4(y) via universal disjunction elimination. Therefore, the answer is yes.