let X, Y be set ; :: thesis: proj1_4 (X /\ Y) c= (proj1_4 X) /\ (proj1_4 Y)
( proj1_4 (X /\ Y) c= proj1_4 X & proj1_4 (X /\ Y) c= proj1_4 Y ) by Th16, XBOOLE_1:17;
hence proj1_4 (X /\ Y) c= (proj1_4 X) /\ (proj1_4 Y) by XBOOLE_1:19; :: thesis: verum