reserve GS for GraphStruct;
reserve G,G1,G2,G3 for _Graph;
reserve e,x,x1,x2,y,y1,y2,E,V,X,Y for set;
reserve n,n1,n2 for Nat;
reserve v,v1,v2 for Vertex of G;

theorem
  for G1, G2 being _Graph, G3 being spanning Subgraph of G1
  st G2 == G3 holds G2 is spanning Subgraph of G1
proof
  let G1, G2 be _Graph, G3 be spanning Subgraph of G1;
  assume A1: G2 == G3;
  then the_Vertices_of G2 = the_Vertices_of G1 by Def33;
  hence thesis by A1, Th92, Def33;
end;
