reserve a,b,c,d for Ordinal;
reserve l for non empty limit_ordinal Ordinal;
reserve u for Element of l;
reserve A for non empty Ordinal;
reserve e for Element of A;
reserve X,Y,x,y,z for set;
reserve n,m for Nat;
reserve f for Ordinal-Sequence;
reserve U,W for Universe;
reserve F,phi for normal Ordinal-Sequence of W;
reserve g for Ordinal-Sequence-valued Sequence;

theorem Th68:
  0-Veblen(a) = exp(omega,a)
  proof
    set b = 0\/a\/omega;
    set U = Tarski-Class b;
    b in U by CLASSES1:2; then
A1: b in On U by ORDINAL1:def 9;
    omega in On U by A1,ORDINAL1:12,XBOOLE_1:7; then
A2: omega in U by ORDINAL1:def 9;
    a in On U by A1,ORDINAL1:12,XBOOLE_1:7; then
A3: a in U by ORDINAL1:def 9;
    thus 0-Veblen(a) = (U exp omega).a by Def15
    .= exp(omega,a) by A3,A2,Def8;
  end;
