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

theorem Th24:
  for G being edgeless _Graph, S being GraphUnionSet, G9 being GraphUnion of S
  st (for v being Vertex of G holds createGraph(v) in S)
  holds G is Subgraph of G9
proof
  let G be edgeless _Graph, S be GraphUnionSet, G9 be GraphUnion of S;
  assume A1: for v being Vertex of G holds createGraph(v) in S;
  now
    let v be Vertex of G;
    reconsider H9 = createGraph(v) as Element of S by A1;
    take H9;
    thus v in the_Vertices_of H9 by TARSKI:def 1;
  end;
  hence thesis by Th22;
end;
