In this paper, we provide a new axiomatization of the event-model-based Dynamic Epistemic Logic, based on the completeness proof method proposed in [Wang and Cao, 2013]. This axiomatization does not use any of the standard reduction axioms, but naturally captures the essence of the update product. We demonstrate the use of our new axiomatization and the corresponding proof techniques by three sets of results: characterization theorems of the update operations, representation theorems of the DEL-generatable epistemic temporal structures given a fixed event model, and a complete axiomatization of DEL on models with protocols.