You don't get the axiom from the theory, it's how you build the theory in the first place. Einstein didn't predict the speed of light was constant, he said it is, and then made predictions based on that assumption. As all his predictions (so far) have been proven correct, science says that his assumptions are correct. Of course someone might one day find evidence that contradicts his theory, in which case his assumption would be in question.
But the implication, and my original statement, is that the speed of light is now defined to be constant. That is, the international standards bodies define other units in terms of the speed of light. By definition it cannot change.