reserve G for _Graph;

theorem Th45:
  for H being Subgraph of G holds VertexAdjSymRel(H) c= VertexAdjSymRel(G)
proof
  let H be Subgraph of G;
  A1: VertexDomRel(H) c= VertexDomRel(G) by Th15;
  then (VertexDomRel(H))~ c= (VertexDomRel(G))~ by SYSREL:11;
  hence thesis by A1, XBOOLE_1:13;
end;
