Theorem nfnan

Description: If x is not free in ph and ps , then it is not free in ( ph -/\ ps ) . (Contributed by Scott Fenton, 2-Jan-2018)

	Ref	Expression
Hypotheses	nfan.1	|- F/ x ph
	nfan.2	|- F/ x ps
Assertion	nfnan	|- F/ x ( ph -/\ ps )

Proof

Step	Hyp	Ref	Expression
1		nfan.1	|- F/ x ph
2		nfan.2	|- F/ x ps
3		df-nan	|- ( ( ph -/\ ps ) <-> -. ( ph /\ ps ) )
4	1 2	nfan	|- F/ x ( ph /\ ps )
5	4	nfn	|- F/ x -. ( ph /\ ps )
6	3 5	nfxfr	|- F/ x ( ph -/\ ps )