Theorem sb8fOLD

Description: Obsolete version of sb8f as of 5-Dec-2024. (Contributed by NM, 16-May-1993) (Revised by Wolf Lammen, 19-Jan-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	sb8f.nf	⊢ Ⅎ 𝑦 𝜑
Assertion	sb8fOLD	⊢ ( ∀ 𝑥 𝜑 ↔ ∀ 𝑦 [ 𝑦 / 𝑥 ] 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		sb8f.nf	⊢ Ⅎ 𝑦 𝜑
2		nfs1v	⊢ Ⅎ 𝑥 [ 𝑦 / 𝑥 ] 𝜑
3		sbequ12	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ [ 𝑦 / 𝑥 ] 𝜑 ) )
4	1 2 3	cbvalv1	⊢ ( ∀ 𝑥 𝜑 ↔ ∀ 𝑦 [ 𝑦 / 𝑥 ] 𝜑 )