Theorem dmxpin

Description: The domain of the intersection of two Cartesian squares. Unlike in dmin , equality holds. (Contributed by NM, 29-Jan-2008)

	Ref	Expression
Assertion	dmxpin	|- dom ( ( A X. A ) i^i ( B X. B ) ) = ( A i^i B )

Proof

Step	Hyp	Ref	Expression
1		inxp	|- ( ( A X. A ) i^i ( B X. B ) ) = ( ( A i^i B ) X. ( A i^i B ) )
2	1	dmeqi	|- dom ( ( A X. A ) i^i ( B X. B ) ) = dom ( ( A i^i B ) X. ( A i^i B ) )
3		dmxpid	|- dom ( ( A i^i B ) X. ( A i^i B ) ) = ( A i^i B )
4	2 3	eqtri	|- dom ( ( A X. A ) i^i ( B X. B ) ) = ( A i^i B )