Theorem sb4vOLD

Description: Obsolete as of 30-Jul-2023. Use sb6 instead. (Contributed by BJ, 23-Jun-2019) (Proof shortened by Steven Nguyen, 8-Jul-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	sb4vOLD	⊢ ( [ 𝑦 / 𝑥 ] 𝜑 → ∀ 𝑥 ( 𝑥 = 𝑦 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		sb6	⊢ ( [ 𝑦 / 𝑥 ] 𝜑 ↔ ∀ 𝑥 ( 𝑥 = 𝑦 → 𝜑 ) )
2	1	biimpi	⊢ ( [ 𝑦 / 𝑥 ] 𝜑 → ∀ 𝑥 ( 𝑥 = 𝑦 → 𝜑 ) )