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_1:19
  {x} (/\) {x,y} = {x}
proof
  now
    let i be object;
    assume
A1: i in I;
    hence ({x} (/\) {x,y}).i = {x}.i /\ {x,y}.i by PBOOLE:def 5
      .= {x.i} /\ {x,y}.i by A1,Def1
      .= {x.i} /\ {x.i,y.i} by A1,Def2
      .= {x.i} by ZFMISC_1:13
      .= {x}.i by A1,Def1;
  end;
  hence {x} (/\) {x,y} = {x};
end;
