Theorem nfs1f

Description: If x is not free in ph , it is not free in [ y / x ] ph . (Contributed by Mario Carneiro, 11-Aug-2016)

	Ref	Expression
Hypothesis	nfs1f.1	|- F/ x ph
Assertion	nfs1f	|- F/ x [ y / x ] ph

Proof

Step	Hyp	Ref	Expression
1		nfs1f.1	|- F/ x ph
2	1	sbf	|- ( [ y / x ] ph <-> ph )
3	2 1	nfxfr	|- F/ x [ y / x ] ph