reserve A,A1,A2,B,B1,B2,C,O for Ordinal,
      R,S for Relation,
      a,b,c,o,l,r for object;

theorem Th5:
  A c= B implies BeforeGames A c= BeforeGames B
proof
  assume A1: A c= B;
  let x,y be object;
  assume [x,y] in BeforeGames A;
  then ex O be Ordinal st O in A & [x,y] in Games O by Def5;
  hence thesis by A1,Def5;
end;
