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	⊢ Ⅎ 𝑥 𝜑
Assertion	nfs1f	⊢ Ⅎ 𝑥 [ 𝑦 / 𝑥 ] 𝜑

Proof

Step	Hyp	Ref	Expression
1		nfs1f.1	⊢ Ⅎ 𝑥 𝜑
2	1	sbf	⊢ ( [ 𝑦 / 𝑥 ] 𝜑 ↔ 𝜑 )
3	2 1	nfxfr	⊢ Ⅎ 𝑥 [ 𝑦 / 𝑥 ] 𝜑