Intersection of kernels of bihomomorphisms implies completely divisibility-closed

Statement
Suppose $$G$$ is a group and $$H$$ is an intersection of kernels of bihomomorphisms in $$G$$. Then, $$H$$ is a completely divisibility-closed subgroup of $$G$$.

Facts used

 * 1) uses::Kernel of a bihomomorphism is completely divisibility-closed
 * 2) uses::Complete divisibility-closedness is strongly intersection-closed

Proof
The proof follows directly from Facts (1) and (2).