It is well-known that the implicational fragment of the classical propositional calculus has a single axiom. By contrast, here we show that the corresponding equational class defined by the implicational reduct of Boolean algebra cannot be defined by a single axiom. However, it can be defined by two identities. By a deep theorem of Alfred Tarski, it follows that this variety has an independent basis with n identities for all n > 1. Furthermore, it follows that no equational theory defined by any of the six well-known orthomodular implications is one-based.