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Metamath Proof Explorer

Theorem unabs

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

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

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