A1: A in bool E by Def2;
A2: A /\ X c= A by XBOOLE_1:17;
A c= E by A1, ZFMISC_1:def 1;
then A /\ X c= E by A2, XBOOLE_1:1;
then A /\ X in bool E by ZFMISC_1:def 1;
hence A /\ X is Subset of E by Def2; :: thesis: verum