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;
reserve A,B for set;
reserve x,y,i,j,k for object;

theorem
  not x in dom f implies f c= f +*(x .--> y)
proof
  assume not x in dom f;
  then dom f misses {x} by ZFMISC_1:50;
  then dom f misses dom(x .--> y);
  hence thesis by Th32;
end;
