Theorem nf3an

Description: If x is not free in ph , ps , and ch , then it is not free in ( ph /\ ps /\ ch ) . (Contributed by Mario Carneiro, 11-Aug-2016)

	Ref	Expression
Hypotheses	nfan.1	|- F/ x ph
	nfan.2	|- F/ x ps
	nfan.3	|- F/ x ch
Assertion	nf3an	|- F/ x ( ph /\ ps /\ ch )

Proof

Step	Hyp	Ref	Expression
1		nfan.1	|- F/ x ph
2		nfan.2	|- F/ x ps
3		nfan.3	|- F/ x ch
4		df-3an	|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
5	1 2	nfan	|- F/ x ( ph /\ ps )
6	5 3	nfan	|- F/ x ( ( ph /\ ps ) /\ ch )
7	4 6	nfxfr	|- F/ x ( ph /\ ps /\ ch )