Well, you have to proceed from those axioms to derive property "rights". I don't believe rights are real. Just something we dilude ourselves into thinking "ought" to exist. These axioms are the only truths. Self interest is revealed through human action. Profit is the effect of two components being joined to create something more than its components or a subjective value scale that aligns between two humans. Competition is just natural human play, has nothing to do with economics.