reserve G, G1, G2 for _Graph, H for Subgraph of G;

theorem Th39:
  [H | _GraphSelectors, G | _GraphSelectors] in SubgraphRel(G)
proof
  A1: H | _GraphSelectors == H & G | _GraphSelectors == G by GLIB_000:128;
  A2: H | _GraphSelectors in G.allSG() &
    G | _GraphSelectors in G.allSG() by Th2, Th3;
  H | _GraphSelectors is Subgraph of G by A1, GLIB_000:92;
  then H| _GraphSelectors is Subgraph of G| _GraphSelectors by A1, GLIB_000:91;
  hence thesis by A2, Def6;
end;
