
theorem Th174:
  for G1 being _Graph, G2 being G1-Disomorphic _Graph
  for G3 being DSimpleGraph of G1, G4 being DSimpleGraph of G2
  holds G4 is G3-Disomorphic
proof
  let G1 be _Graph, G2 be G1-Disomorphic _Graph;
  let G3 be DSimpleGraph of G1, G4 be DSimpleGraph of G2;
  set G5 = the removeLoops of G1, G6 = the removeLoops of G2;
  A1: G6 is G5-Disomorphic by Th167;
  G3 is removeDParallelEdges of G5 & G4 is removeDParallelEdges of G6
    by GLIB_009:122;
  hence thesis by A1, Th170;
end;
