Theorem nfdif

Description: Bound-variable hypothesis builder for class difference. (Contributed by NM, 3-Dec-2003) (Revised by Mario Carneiro, 13-Oct-2016)

	Ref	Expression
Hypotheses	nfdif.1	|- F/_ x A
	nfdif.2	|- F/_ x B
Assertion	nfdif	|- F/_ x ( A \ B )

Proof

Step	Hyp	Ref	Expression
1		nfdif.1	|- F/_ x A
2		nfdif.2	|- F/_ x B
3		dfdif2	|- ( A \ B ) = { y e. A | -. y e. B }
4	2	nfcri	|- F/ x y e. B
5	4	nfn	|- F/ x -. y e. B
6	5 1	nfrabw	|- F/_ x { y e. A | -. y e. B }
7	3 6	nfcxfr	|- F/_ x ( A \ B )