 Due to the monotonicity property of the Leibniz operator, for every protoalgebraic logic \(\bL\) the class of algebras \(\bAlg^*\bL\) is closed under subdirect products and therefore it is equal to \(\bAlg\bL\). Hence, for protoalgebraic logics the two ways we encountered to associate a class of algebras with a logic produce, as we already mentioned, the same result.