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_1:52
  x in X implies X (/\) {x} = {x}
proof
  assume
A1: x in X;
  now
    let i be object;
    assume
A2: i in I;
    then
A3: x.i in X.i by A1;
    thus (X (/\) {x}).i = X.i /\ {x}.i by A2,PBOOLE:def 5
      .= X.i /\ {x.i} by A2,Def1
      .= {x.i} by A3,ZFMISC_1:46
      .= {x}.i by A2,Def1;
  end;
  hence X (/\) {x} = {x};
end;
