let U be set ; :: thesis: for A, B being Subset of U st Inter A,B <> {} holds
A c= B
let A, B be Subset of U; :: thesis: ( Inter A,B <> {} implies A c= B )
assume Inter A,B <> {} ; :: thesis: A c= B
then consider x being set such that
A1: x in Inter A,B by XBOOLE_0:def 1;
( A c= x & x c= B ) by A1, Lemacik;
hence A c= B by XBOOLE_1:1; :: thesis: verum