theorem
  omega in W implies ex a,M st a is_cofinal_with omega & M = Rank a & M
  is being_a_model_of_ZF
proof
  assume
A1: omega in W;
  then consider a,M such that
A2: a is_cofinal_with omega & M = Rank a & M <==> W by Th39;
  take a,M;
  W is being_a_model_of_ZF by A1,ZF_REFLE:6;
  hence thesis by A2,Th10;
end;
