theorem Th45:
  dom f c= [:X,Y:] implies dom ~f c= [:Y,X:]
proof
  assume
A1: dom f c= [:X,Y:];
  let z be object;
  assume z in dom ~f;
  then ex x,y being object st z = [y,x] & [x,y] in dom f by Def2;
  hence thesis by A1,ZFMISC_1:88;
end;
