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_1:6
  {x} = {y} implies x = y
proof
  assume
A1: {x} = {y};
  now
    let i be object;
    assume
A2: i in I;
    then {x.i} = {x}.i by Def1
      .= {y.i} by A1,A2,Def1;
    hence x.i = y.i by ZFMISC_1:3;
  end;
  hence thesis;
end;
