Is there anything wrong with doing this after brushing teeth?

Sorry, I had absolutely no idea how to phrase this question.

So, after I brush my teeth, I always rinse my mouth of the toothpaste by running my toothbrush under the water then brushing my teeth with just water until my mouth is rinsed.

Does this take away from the actual brushing? Am I just removing all the cleaning and protection that I just put on my teeth? Or does the toothpaste still “work its magic?” I only just thought of this this morning after brushing, and I got kind of worried that my entire life I’ve just been canceling all the cleaning I’ve done…. :(