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.