Theorem nfin

Description: Bound-variable hypothesis builder for the intersection of classes. (Contributed by NM, 15-Sep-2003) (Revised by Mario Carneiro, 14-Oct-2016)

	Ref	Expression
Hypotheses	nfin.1	|- F/_ x A
	nfin.2	|- F/_ x B
Assertion	nfin	|- F/_ x ( A i^i B )

Proof

Step	Hyp	Ref	Expression
1		nfin.1	|- F/_ x A
2		nfin.2	|- F/_ x B
3		dfin5	|- ( A i^i B ) = { y e. A | y e. B }
4	2	nfcri	|- F/ x y e. B
5	4 1	nfrabw	|- F/_ x { y e. A | y e. B }
6	3 5	nfcxfr	|- F/_ x ( A i^i B )