let X, Y be set ; :: thesis: (proj2_3 X) \+\ (proj2_3 Y) c= proj2_3 (X \+\ Y)
( (proj2_3 X) \ (proj2_3 Y) c= proj2_3 (X \ Y) & (proj2_3 Y) \ (proj2_3 X) c= proj2_3 (Y \ X) ) by Th37;
then (proj2_3 X) \+\ (proj2_3 Y) c= (proj2_3 (X \ Y)) \/ (proj2_3 (Y \ X)) by XBOOLE_1:13;
hence (proj2_3 X) \+\ (proj2_3 Y) c= proj2_3 (X \+\ Y) by Th35; :: thesis: verum