B in bool E by Def2;
then A2: B c= E by ZFMISC_1:def 1;
A in bool E by Def2;
then A c= E by ZFMISC_1:def 1;
then A \/ B c= E by A2, 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