reserve x,y,z for Variable,
  H for ZF-formula,
  E for non empty set,
  a,b,c,X,Y,Z for set,
  u,v,w for Element of E,
  f,g,h,i,j for Function of VAR,E;

theorem
  E is being_a_model_of_ZF implies E is epsilon-transitive & (for u,v st
  for w holds w in u iff w in v holds u = v) & (for u,v holds { u,v } in E) & (
for u holds union u in E) & (ex u st u <> {} & for v st v in u ex w st v c< w &
  w in u) & (for u holds E /\ bool u in E) & for H,f st { x.0,x.1,x.2 } misses
  Free H & E,f |= All(x.3,Ex(x.0,All(x.4,H <=> x.4 '=' x.0))) for u holds
  def_func'(H,f).:u in E
by Lm3,Th2,Th4,Th6,Th8,Th15;
