( A in bool E & B in bool E ) by Def2;
then ( A c= E & B c= E ) by ZFMISC_1:def 1;
then A \/ B 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