
theorem Th47:
  for G1, G2 being non-multi _Graph, f being PVertexMapping of G1, G2
  st f is isomorphism holds PVM2PGM(f) is isomorphism
proof
  let G1, G2 be non-multi _Graph, f being PVertexMapping of G1, G2;
  assume f is isomorphism;
  then PVM2PGM(f) is total one-to-one onto by Th32, Th34, Th36;
  hence thesis;
end;
