Here's the formulation for group theory; replace "group" by whatever to get it in other domains (it usually holds whenever it may be formulated).

Let G be a group, H a normal subgroup of G, and N a normal subgroup of G which is also a subgroup of H. Then

(G/N) / (H/N)

is isomorphic to G/H.

Note that the example of a normal subgroup of a normal subgroup which is not normal shows why we cannot just take N normal in H.

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