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_1:13
  {x} (\/) {y} = {x} implies x = y
proof
  assume
A1: {x} (\/) {y} = {x};
  now
    let i be object such that
A2: i in I;
      {x.i} \/ {y.i} = {x.i} \/ {y}.i by A2,Def1
        .= {x}.i \/ {y}.i by A2,Def1
        .= ({x} (\/) {y}).i by A2,PBOOLE:def 4
        .= {x.i} by A2,A1,Def1;
      hence x.i = y.i by ZFMISC_1:8;
  end;
  hence thesis;
end;
