  We present a short proof of a celebrated result of G\'acs and K\"orner giving
sufficient and necessary condition on the joint distribution of two discrete
random variables $X$ and $Y$ for the case when their mutual information matches
the extractable (in the limit) common information. Our proof is based on the
observation that the mere existence of certain random variables jointly
distributed with $X$ and $Y$ can impose restriction on all random variables
jointly distributed with $X$ and $Y$.
