reserve p,q,x,x1,x2,y,y1,y2,z,z1,z2 for set;
reserve A,B,V,X,X1,X2,Y,Y1,Y2,Z for set;
reserve C,C1,C2,D,D1,D2 for non empty set;

theorem
  for f being Function of X,Y for g being Function of X,Z holds rng <:f,
  g:> c= [:Y,Z:]
proof
  let f be Function of X,Y;
  let g be Function of X,Z;
  rng f c= Y & rng g c= Z by RELAT_1:def 19;
  then
A1: [:rng f,rng g:] c= [:Y,Z:] by ZFMISC_1:96;
  rng <:f,g:> c= [:rng f,rng g:] by Th51;
  hence thesis by A1;
end;
