Unlikely formal intersections

Let $G$ be an algebraic group over a field of characteristic $0$, $A$ an analytic (or formal) subgroup of $G$ and $V$ an algebraic subvariety of $G$. Ax proved that if the intersection of $A$ and $V$ is Zariski dense in $V$, then $A$ and $V$ tend to be in general position. I will discuss a theorem involving formal maps which implies Ax's theorem and also covers some cases in the positive characteristic situation.