# Name for DNF simplification rule / prime implicants under closure?

I was reading this question which links to this list of propositional equivalences.

One of the equivalences shown (T5a) is:

$$A \wedge B \vee A \wedge \neg B \equiv A$$

I have used this rule by intuition in the past, but never put a name to it. I was wondering if it has a formal name?

Further I wonder (and perhaps this should be a separate question), if I were to close a DNF formula under this rule (inefficient as this may be), would I find the prime implicants? Does any paper/book describe such a process?

Thanks

$$(A\land B) \lor (A \land \lnot B) \equiv A\land (B \lor \lnot B) \equiv A \land 1 \equiv A$$
That is, it's justified (can be proven to hold) by an application of the distributive law, and the facts that $B\lor\lnot B = 1\;$ (by T10), and $\;A\land 1 = A\;$ (by T8)