A2: ( A in bool E & B in bool E ) by Def2;
A3: ( A \ B c= A & B \ A c= B ) by XBOOLE_1:36;
( A c= E & B c= E ) by A2, ZFMISC_1:def 1;
then ( A \ B c= E & B \ A c= E ) by A3, XBOOLE_1:1;
then (A \ B) \/ (B \ A) c= E by XBOOLE_1:8;
then A \+\ B in bool E by ZFMISC_1:def 1;
hence A \+\ B is Subset of E by Def2; :: thesis: verum