reserve a,a1,a2,b,c,d for Ordinal,
  n,m,k for Nat,
  x,y,z,t,X,Y,Z for set;

theorem Th4:
  (succ x)\x = {x}
  proof
    not x in x; then
    succ x = x\/{x} & x nin x;
    hence thesis by XBOOLE_1:88,ZFMISC_1:50;
  end;
