reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;

theorem Th59:
  for f being PartFunc of [:X,Y:],Z for g being PartFunc of [:X9,Y9:],Z9
  holds |:f,g:| is PartFunc of [:[:X,X9:],[:Y,Y9:]:],[:Z,Z9:]
proof
  let f be PartFunc of [:X,Y:],Z;
  let g be PartFunc of [:X9,Y9:],Z9;
  rng |:f,g:| c= [:rng f,rng g:] & [:rng f,rng g:] c= [:Z,Z9:] by Th56,
ZFMISC_1:96;
  then
A1: rng|:f,g:| c= [:Z,Z9:];
  dom f c= [:X,Y:] & dom g c= [:X9,Y9:];
  then dom|:f,g:| c= [:[:X,X9:],[:Y,Y9:]:] by Th57;
  hence thesis by A1,RELSET_1:4;
end;
