theorem Th10:
  M1 is being_a_model_of_ZF & M1 <==> M2 & M2 is
  epsilon-transitive implies M2 is being_a_model_of_ZF
proof
  assume that
A1: M1 is being_a_model_of_ZF and
A2: M1 <==> M2;
  M1 |= ZF-axioms by A1,Th4;
  then M2 |= ZF-axioms by A2,Th8;
  hence thesis by Th5;
end;
