Theorem inabs

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

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

Proof

Step	Hyp	Ref	Expression
1		ssun1	$$⊢A\subseteq A\cup B$$
2		dfss2	$$⊢A\subseteq A\cup B\leftrightarrow A\cap \left(A\cup B\right)=A$$
3	1 2	mpbi	$$⊢A\cap \left(A\cup B\right)=A$$