Theorem nfsbOLD

Description: Obsolete version of nfsb as of 25-Feb-2024. (Contributed by Mario Carneiro, 11-Aug-2016) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	nfsb.1	⊢ Ⅎ 𝑧 𝜑
Assertion	nfsbOLD	⊢ Ⅎ 𝑧 [ 𝑦 / 𝑥 ] 𝜑

Proof

Step	Hyp	Ref	Expression
1		nfsb.1	⊢ Ⅎ 𝑧 𝜑
2		axc16nf	⊢ ( ∀ 𝑧 𝑧 = 𝑦 → Ⅎ 𝑧 [ 𝑦 / 𝑥 ] 𝜑 )
3	1	nfsb4	⊢ ( ¬ ∀ 𝑧 𝑧 = 𝑦 → Ⅎ 𝑧 [ 𝑦 / 𝑥 ] 𝜑 )
4	2 3	pm2.61i	⊢ Ⅎ 𝑧 [ 𝑦 / 𝑥 ] 𝜑