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	$$⊢Ⅎx\phi$$
Assertion	nfs1f	$$⊢Ⅎx\left[y/x\right]\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfs1f.1	$$⊢Ⅎx\phi$$
2	1	sbf	$$⊢\left[y/x\right]\phi \leftrightarrow \phi$$
3	2 1	nfxfr	$$⊢Ⅎx\left[y/x\right]\phi$$