reserve a,x,y for object, A,B for set,
  l,m,n for Nat;

theorem
  for x,y be set, A be set st x <> y holds not x in rng(id A +* (x .-->
  y))
proof
  let x,y be set, A be set;
  assume x <> y;
  then not y in {x} by TARSKI:def 1;
  then {x} misses rng(id A +* ({x} --> y)) by Th12;
  hence thesis by ZFMISC_1:48;
end;
