reserve H,S for ZF-formula,
  x for Variable,
  X,Y for set,
  i for Element of NAT,
  e,u for set;
reserve M,M1,M2 for non empty set,
  f for Function,
  v1 for Function of VAR,M1,
  v2 for Function of VAR,M2,
  F,F1,F2 for Subset of WFF,
  W for Universe,
  a,b,c for Ordinal of W,
  A,B,C for Ordinal,
  L for DOMAIN-Sequence of W,
  va for Function of VAR,L.a,
  phi,xi for Ordinal-Sequence of W;
reserve psi for Ordinal-Sequence;

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;
