let X, Y be set ; :: thesis: (proj2 X) \+\ (proj2 Y) c= proj2 (X \+\ Y)
( (proj2 X) \ (proj2 Y) c= proj2 (X \ Y) & (proj2 Y) \ (proj2 X) c= proj2 (Y \ X) ) by Th29;
then (proj2 X) \+\ (proj2 Y) c= (proj2 (X \ Y)) \/ (proj2 (Y \ X)) by XBOOLE_1:13;
hence (proj2 X) \+\ (proj2 Y) c= proj2 (X \+\ Y) by Th27; :: thesis: verum