reserve x,y for set;

theorem
  for f, g being Function st dom f is Relation & ~f c= ~g holds f c= g
proof
  let f, g be Function;
  assume dom f is Relation;
  then reconsider R = dom f as Relation;
  R c= [:dom R, rng R:] by RELAT_1:7;
  then
A1: ~~f = f by FUNCT_4:52;
  assume ~f c= ~g;
  then ~~g c= g & f c= ~~g by A1,Th44,FUNCT_4:51;
  hence thesis;
end;
