  A simple and general proof is given for the information theoretic
(unconditional) security of the Kirchhoff-law-Johnson-noise (KLJN) key exchange
system under practical conditions. The unconditional security for ideal
circumstances, which is based on the Second Law of Thermodynamics, is found to
prevail even under slightly non-ideal conditions. This security level is
guaranteed by the continuity of functions describing classical physical linear,
as well as stable non-linear, systems. Even without privacy amplification,
Eve's probability for successful bit-guessing is found to converge towards 0.5
- i.e., the perfect security level - when ideal conditions are approached.
