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 Th62:
  ex A st X c= Rank A
proof
  consider A such that
A1: Tarski-Class the_transitive-closure_of X c= Rank A by Th47;
  take A;
 the_transitive-closure_of X in Tarski-Class the_transitive-closure_of X
  by Th2;
then  X in Tarski-Class the_transitive-closure_of X by Th3,Th52;
  hence thesis by A1,ORDINAL1:def 2;
end;
