
theorem Th172:
  for G1 being _Graph, G2 being G1-isomorphic _Graph
  for G3 being SimpleGraph of G1, G4 being SimpleGraph of G2
  holds G4 is G3-isomorphic
proof
  let G1 be _Graph, G2 be G1-isomorphic _Graph;
  let G3 be SimpleGraph of G1, G4 be SimpleGraph of G2;
  set G5 = the removeLoops of G1, G6 = the removeLoops of G2;
  A1: G6 is G5-isomorphic by Th166;
  G3 is removeParallelEdges of G5 & G4 is removeParallelEdges of G6
    by GLIB_009:121;
  hence thesis by A1, Th168;
end;
