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 Th99:
 for x,y being object holds
  dom(f+~(x,y)) = dom f
proof let x,y be object;
  thus dom(f+~(x,y)) = dom f \/ dom((x .--> y)*f) by Def1
    .= dom f by RELAT_1:25,XBOOLE_1:12;
end;
