for R being Relation holds
( ( R c= R * R & R * (R \ (id (rng R))) = {} implies R /\ (id (rng R)) = id (rng R) ) & ( R c= R * R & (R \ (id (dom R))) * R = {} implies R /\ (id (dom R)) = id (dom R) ) ) by Th22, XBOOLE_1:28;