does individually strategy proof implies coalitionally strategy proof?

Question

Suppose $F$ is a social choice function \begin{equation*}F:N\rightarrow A\end{equation*} where $N=\{1,...,n\}$ is the set of agents and $A$ is a finite set of outcomes.
suppose that $F$ is individually strategy proof, does it imply that $F$ is also coalitionally strategy proof?
edit: I think I can prove it using an argument on $\mbox{Im}(F)$, similar to the Muller-Satterthwaite theorem (for the case $|A|\ge3$). and a preety simple argument for the case $|A|<3$.
This method is not very elegant and spectacular as one might expect from such claim. Is there any other way of proving it?