reserve
  a,b,c,d,e for Ordinal,
  m,n for Nat,
  f for Ordinal-Sequence,
  x for object;
reserve S,S1,S2 for Sequence;

theorem Th38:
  for e being epsilon Ordinal holds
  exp(omega, exp(e, omega)) = exp(e, exp(e, omega))
  proof
    let e be epsilon Ordinal;
    thus exp(omega, exp(e, omega)) = exp(omega, exp(e, 1+^omega)) by CARD_2:74
    .= exp(omega, exp(e, omega)*^exp(e, 1)) by ORDINAL4:30
    .= exp(omega, exp(e, omega)*^e) by ORDINAL2:46
    .= exp(exp(omega, e), exp(e, omega)) by ORDINAL4:31
    .= exp(e, exp(e, omega)) by Def5;
  end;
