reserve G for _Graph;

theorem Th15:
  for H being Subgraph of G holds VertexDomRel(H) c= VertexDomRel(G)
proof
  let H be Subgraph of G;
  now
    let v,w be object;
    assume [v,w] in VertexDomRel(H);
    then consider e being object such that
      A1: e DJoins v,w,H by Th1;
    e is set & v is set & w is set by TARSKI:1;
    then e DJoins v,w,G by A1, GLIB_000:72;
    hence [v,w] in VertexDomRel(G) by Th1;
  end;
  hence thesis by RELAT_1:def 3;
end;
