Theorem unabs

Description: Absorption law for union. (Contributed by NM, 16-Apr-2006)

	Ref	Expression
Assertion	unabs	$$⊢A\cup \left(A\cap B\right)=A$$

Proof

Step	Hyp	Ref	Expression
1		inss1	$$⊢A\cap B\subseteq A$$
2		ssequn2	$$⊢A\cap B\subseteq A\leftrightarrow A\cup \left(A\cap B\right)=A$$
3	1 2	mpbi	$$⊢A\cup \left(A\cap B\right)=A$$