Theorem undif2

Description: Absorption of difference by union. This decomposes a union into two disjoint classes (see disjdif ). Part of proof of Corollary 6K of Enderton p. 144. (Contributed by NM, 19-May-1998)

	Ref	Expression
Assertion	undif2	|- ( A u. ( B \ A ) ) = ( A u. B )

Proof

Step	Hyp	Ref	Expression
1		uncom	|- ( A u. ( B \ A ) ) = ( ( B \ A ) u. A )
2		undif1	|- ( ( B \ A ) u. A ) = ( B u. A )
3		uncom	|- ( B u. A ) = ( A u. B )
4	1 2 3	3eqtri	|- ( A u. ( B \ A ) ) = ( A u. B )