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

theorem Th3:
  for U being set, A, B being Subset of U st not A c= B holds Inter (A, B) = {}
  proof
    let U be set, A, B be Subset of U;
    assume
A1: not A c= B;
    assume Inter (A, B) <> {}; then
    consider x being object such that
A2: x in Inter (A, B) by XBOOLE_0:def 1;
    reconsider x as set by TARSKI:1;
    A c= x & x c= B by A2,Th1;
    hence thesis by A1;
  end;
