Theorem nfdifOLD

Description: Obsolete version of nfdif as of 14-May-2025. (Contributed by NM, 3-Dec-2003) (Revised by Mario Carneiro, 13-Oct-2016) (Proof modification is discouraged.) (New usage is discouraged.)

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