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;
reserve U for uncountable Universe;

theorem
  1-Veblen(a) = epsilon_a
  proof set U = Tarski-Class(a\/omega);
    defpred P[Ordinal] means 1-Veblen $1 = epsilon_$1;
A1: P[0] by Lm4;
A2: P[b] implies P[succ b] by Lm5;
A3: b <> 0 & b is limit_ordinal & (for c st c in b holds P[c]) implies P[b]
    by Lm6;
    P[b] from ORDINAL2:sch 1(A1,A2,A3);
    hence thesis;
  end;
