Equivalent Definitions of Finite Groups of Lie type

Question

I am reading Carter's book on finite groups of lie type and am looking for a reference, or maybe a hint on the following statement in the introduction. He defines a finite group of lie type as the fixed points of a Steinberg endomorphism $F: G \to G$ where $G$ is a reductive group over an algebraically closed field of characteristic p. In Carter's book, and in this math overflow question: https://mathoverflow.net/questions/136880/definition-of-finite-group-of-lie-type it is claimed that this definition is equivalent to admitting a BN pair. Does anyone know how to prove that these two definitions are equivalent?