
theorem
  for G1, G2 being non-multi _Graph holds G2 is G1-isomorphic iff
    ex f being PVertexMapping of G1, G2 st f is isomorphism
proof
  let G1, G2 be non-multi _Graph;
  hereby
    assume G2 is G1-isomorphic;
    then consider F being PGraphMapping of G1, G2 such that
      A1: F is isomorphism by GLIB_010:def 23;
    consider f being PVertexMapping of G1, G2 such that
      A2: F_V = f & f is isomorphism by A1, Th25;
    take f;
    thus f is isomorphism by A2;
  end;
  given f being PVertexMapping of G1, G2 such that
    A3: f is isomorphism;
  PVM2PGM f is isomorphism by A3, Th47;
  hence thesis by GLIB_010:def 23;
end;
