Definition:Mutatis Mutandis

Definition
Mutatis mutandis is Latin for "what needs changing having been changed".

It can be used in place of words like analogously and similarly, and expresses that an argument can be applied to a new situation in an intuitive fashion.

For example the proof of Union is Associative can be made into that for Intersection is Associative by mutatis mutandis.

In this case, this comes down to replacing $\cup$ by $\cap$, and $\lor$ by $\land$.

In particular, the essential flow of the argument wasn't changed in adapting the proof.