symbolize and prove the arguments below

Moral principles are simply a function of human needs and interests (F).  If that's true and if some moral principles would meet human needs and interests better than others (B), then there are at least some objectively valid moral principles (P) and Objectivism is true (O).  Further, I would argue that some moral principles do meet our needs and interests as humans better than others do; thus there are at least some objectively valid moral principles.