Theorem nfcvf

Description: If x and y are distinct, then x is not free in y . Usage of this theorem is discouraged because it depends on ax-13 . See nfcv for a version that replaces the distinctor with a disjoint variable condition, requiring fewer axioms. (Contributed by Mario Carneiro, 8-Oct-2016) Avoid ax-ext . (Revised by Wolf Lammen, 10-May-2023) (New usage is discouraged.)

	Ref	Expression
Assertion	nfcvf	|- ( -. A. x x = y -> F/_ x y )

Proof

Step	Hyp	Ref	Expression
1		nfv	|- F/ w -. A. x x = y
2		nfv	|- F/ x w e. z
3		elequ2	|- ( z = y -> ( w e. z <-> w e. y ) )
4	2 3	dvelimnf	|- ( -. A. x x = y -> F/ x w e. y )
5	1 4	nfcd	|- ( -. A. x x = y -> F/_ x y )