reserve G for _Graph;
reserve G2 for _Graph, G1 for Supergraph of G2;

theorem Th74:
  for G2, G1 for x,y being set, e being object holds
    (e Joins x,y,G2 implies e Joins x,y,G1) &
    (e DJoins x,y,G2 implies e DJoins x,y,G1) &
    (e SJoins x,y,G2 implies e SJoins x,y,G1) &
    (e DSJoins x,y,G2 implies e DSJoins x,y,G1)
proof
  let G2, G1;
  let x,y be set;
  let e be object;
  G2 is Subgraph of G1 by Th61;
  hence thesis by GLIB_000:72;
end;
