theorem Th6:
  omega in W implies W is being_a_model_of_ZF
proof
  assume omega in W;
  hence W is epsilon-transitive & W |= the_axiom_of_pairs & W |=
the_axiom_of_unions & W |= the_axiom_of_infinity & W |= the_axiom_of_power_sets
  & for H st { x.0,x.1,x.2 } misses Free H holds W |=
  the_axiom_of_substitution_for H by Th1,Th2,Th3,Th4,Th5;
end;
