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

theorem     :: ENUMSET1:9
  x = A or x = B implies x in { A,B }
proof
  assume
A1: x=A or x=B;
  per cases by A1;
  suppose
A2: x=A;
    let i such that
A3: i in I;
    x.i in {A.i,B.i} by A2,TARSKI:def 2;
    hence thesis by A3,Def2;
  end;
  suppose
A4: x=B;
    let i such that
A5: i in I;
    x.i in {A.i,B.i} by A4,TARSKI:def 2;
    hence thesis by A5,Def2;
  end;
end;
