reserve X,Y,Z for set,
        x,y,z for object,
        A,B,C for Ordinal;
reserve U for Grothendieck;

theorem :: Theorem 2 (1)
  x in X & y in Rrank x implies y in Rrank X
proof
  assume
A1: x in X & y in Rrank x;
  reconsider x,y as set by TARSKI:1;
  the_rank_of x in the_rank_of X by A1,CLASSES1:68;
  then Rrank x c= Rrank X by ORDINAL1:def 2,CLASSES1:36;
  hence thesis by A1;
end;
