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 Th103:
 for x,y being object holds
  not x in rng f implies f+~(x,y) = f
proof let x,y be object;
  assume not x in rng f;
  then dom (x .--> y) misses rng f by ZFMISC_1:50;
  then (x .--> y)*f = {} by RELAT_1:44;
  hence thesis;
end;
