reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem
  for f being PartFunc of X,Y holds f|Z is PartFunc of Z,Y
proof
  let f be PartFunc of X,Y;
  dom(f|Z) c= Z & rng(f|Z) c= Y by RELAT_1:58,def 19;
  hence thesis by RELSET_1:4;
end;
