
theorem Th133:
  for G1 being _Graph, G2 being DSimpleGraph of G1, G3 being SimpleGraph of G2
  holds G3 is SimpleGraph of G1
proof
  let G1 be _Graph, G2 be DSimpleGraph of G1, G3 be SimpleGraph of G2;
  set H = the removeLoops of G1;
  G2 is removeDParallelEdges of H & G3 is removeParallelEdges of G2
    by Th122, Th123;
  then G3 is removeParallelEdges of H by Th95;
  hence thesis by Th117;
end;
