reserve i for object, I for set,
  f for Function,
  x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I;

theorem     :: ZFMISC_1:21
  {x} (\) {y} = EmptyMS I implies x = y
proof
  assume
A1: {x} (\) {y} = EmptyMS I;
  now
    let i be object;
    assume
A2: i in I;
    then {x.i} \ {y.i} = {x}.i \ {y.i} by Def1
      .= {x}.i \ {y}.i by A2,Def1
      .= ({x} (\) {y}).i by A2,PBOOLE:def 6
      .= {} by A1,PBOOLE:5;
    hence x.i = y.i by ZFMISC_1:15;
  end;
  hence thesis;
end;
