reserve x,y,y1,y2,z,a,b for object, X,Y,Z,V1,V2 for set,
  f,g,h,h9,f1,f2 for Function,
  i for Nat,
  P for Permutation of X,
  D,D1,D2,D3 for non empty set,
  d1 for Element of D1,
  d2 for Element of D2,
  d3 for Element of D3;

theorem Th18:
 for f being Function-yielding Function holds
  x in dom f & g = f.x implies x in dom doms f & (doms f).x = dom
  g & x in dom rngs f & (rngs f).x = rng g
by Def1,Def2;
