let X1, X2, X3 be set ; :: thesis: ( not X1 in X2 or not X2 in X3 or not X3 in X1 )
A1: ( X2 in {X1,X2,X3} & X3 in {X1,X2,X3} ) by ENUMSET1:def 1;
A2: X1 in {X1,X2,X3} by ENUMSET1:def 1;
then consider T being set such that
A3: T in {X1,X2,X3} and
A4: {X1,X2,X3} misses T by Th1;
( T = X1 or T = X2 or T = X3 ) by A3, ENUMSET1:def 1;
hence ( not X1 in X2 or not X2 in X3 or not X3 in X1 ) by A2, A1, A4, XBOOLE_0:3; :: thesis: verum