  For $n \geq 2$ let $\Delta$ be a Dynkin diagram of rank $n$ and let $I = {1,
>..., n}$ be the set of labels of $\Delta$. A group $G$ admits a weak Phan
system of type $\Delta$ over $\mathbb{C}$ if $G$ is generated by subgroups
$U_i$, $i \in I$, which are central quotients of simply connected compact
semisimple Lie groups of rank one, and contains subgroups $U_{i,j} = \gen{U_i
,U_j}$, $i \neq j \in I$, which are central quotients of simply connected
compact semisimple Lie groups of rank two such that $U_i$ and $U_j$ are rank
one subgroups of $U_{i,j}$ corresponding to a choice of a maximal torus and a
fundamental system of roots for $U_{i,j}$. It is shown in this article that $G$
then is a central quotient of the simply connected compact semisimple Lie group
whose complexification is the simply connected complex semisimple Lie group of
type $\Delta$.
