reserve A,A1,A2,B,C,D for Ordinal,
  X,Y for set,
  x,y,a,b,c for object,
  L,L1,L2,L3 for Sequence,
  f for Function;

theorem Th2:
  union succ A = A
proof
  thus union succ A c= A
  proof
    let x be object;
    assume x in union succ A;
    then consider X such that
A1: x in X and
A2: X in succ A by TARSKI:def 4;
    reconsider X as Ordinal by A2;
    X c= A by A2,ORDINAL1:22;
    hence thesis by A1;
  end;
  thus thesis by ORDINAL1:6,ZFMISC_1:74;
end;
