 reserve U for set,
         X, Y for Subset of U;

theorem Th5:
  for A, B being Subset of U st Inter (A, B) <> {} holds A c= B
  proof
    let A, B be Subset of U;
    assume Inter (A, B) <> {}; then
    consider x being object such that
A1: x in Inter (A, B) by XBOOLE_0:def 1;
    reconsider x as set by TARSKI:1;
    A c= x & x c= B by A1,Th1;
    hence thesis;
  end;
