Quotient of amalgamated free product by amalgamated normal subgroup equals free product of quotient groups

Statement
Suppose $$G_1$$ and $$G_2$$ are two groups containing a common subgroup $$H$$ that is a normal subgroup in both. Suppose $$L = G_1 *_H G_2$$ is the external amalgamated free product of $$G_1$$ and $$G_2$$ over $$H$$. Then, the amalgamated subgroup $$H$$ is normal in $$L$$, and $$L/H \cong G_1/H * G_2/H$$.