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**.