reserve G for _Graph;

theorem Th33:
  for v, w being Vertex of G
  holds [v,w] in VertexAdjSymRel(G) iff v, w are_adjacent
proof
  let v, w be Vertex of G;
  hereby
    assume [v,w] in VertexAdjSymRel(G);
    then consider e being object such that
      A1: e Joins v,w,G by Th32;
    thus v,w are_adjacent by A1, CHORD:def 3;
  end;
  assume v,w are_adjacent;
  then consider e being object such that
    A2: e Joins v,w,G by CHORD:def 3;
  thus [v,w] in VertexAdjSymRel(G) by A2, Th32;
end;
