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

theorem Th129:
  H.allConnectedSG() c= G.allConnectedSG()
proof
  now
    let x be object;
    assume x in H.allConnectedSG();
    then reconsider H9 = x as plain connected Subgraph of H by Th124;
    H9 is Subgraph of G by GLIB_000:43;
    hence x in G.allConnectedSG() by Th124;
  end;
  hence thesis by TARSKI:def 3;
end;
