reserve E, x, y, X for set;
reserve A, B, C for Subset of E^omega;
reserve a, b for Element of E^omega;
reserve i, k, l, kl, m, n, mn for Nat;

theorem Th80:
  A? = A iff <%>E in A
proof
  thus A? = A implies <%>E in A
  proof
    assume A? = A;
    then A = {<%>E} \/ A by Th76;
    hence thesis by ZFMISC_1:39;
  end;
  assume <%>E in A;
  then A = {<%>E} \/ A by ZFMISC_1:40;
  hence thesis by Th76;
end;
