let X, Y be set ; :: thesis: proj2_3 (X /\ Y) c= (proj2_3 X) /\ (proj2_3 Y)
( proj2_3 (X /\ Y) c= proj2_3 X & proj2_3 (X /\ Y) c= proj2_3 Y ) by Th11, XBOOLE_1:17;
hence proj2_3 (X /\ Y) c= (proj2_3 X) /\ (proj2_3 Y) by XBOOLE_1:19; :: thesis: verum