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

theorem Th7:
  for U being non empty set, A being non empty Subset of U holds
    Inter (A, {}U) = {}
  proof
    let U be non empty set,
        A be non empty Subset of U;
    thus Inter (A,{}U) c= {}
    proof
      let x be object;
     reconsider xx=x as set by TARSKI:1;
      assume x in Inter (A,{}U); then
      A c= xx & xx c= {}U by Th1;
      hence thesis;
    end;
    thus thesis;
  end;
