reserve W,X,Y,Z for set,
  f,g for Function,
  a,x,y,z for set;
reserve u,v for Element of Tarski-Class(X),
  A,B,C for Ordinal,
  L for Sequence;
reserve n for Element of omega;

theorem Th72:
  the_rank_of X = succ A implies ex Y st Y in X & the_rank_of Y = A
proof
  assume
A1: the_rank_of X = succ A;
  consider Y such that
A2: Y in X and
A3: A c= the_rank_of Y by A1,Th70,ORDINAL1:6;
  take Y;
  the_rank_of Y c= A by A1,ORDINAL1:22,A2,Th68;
  hence thesis by A2,A3;
end;
