Intersection of kernels of bihomomorphisms implies completely divisibility-closed

This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., intersection of kernels of bihomomorphisms) must also satisfy the second subgroup property (i.e., completely divisibility-closed subgroup)
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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. Kernel of a bihomomorphism implies completely divisibility-closed
2. Complete divisibility-closedness is strongly intersection-closed

Proof

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