It seems that you do have that result, see here: http://link.springer.com/article/10.1007%2FBF01766393
However this seems to require a strengthening of the independence axiom, so that the implication goes in the opposite direction in some cases (see axiom 6, page 71).
It seems that you do have that result, see here: http://link.springer.com/article/10.1007%2FBF01766393
However this seems to require a strengthening of the independence axiom, so that the implication goes in the opposite direction in some cases (see axiom 6, page 71).