Theorem sb2vOLD

Description: Obsolete as of 30-Jul-2023. Use sb6 instead. Version of sb2 with a disjoint variable condition, which does not require ax-13 . (Contributed by BJ, 31-May-2019) Revise df-sb . (Revised by Steven Nguyen, 8-Jul-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	sb2vOLD	⊢ ( ∀ 𝑥 ( 𝑥 = 𝑦 → 𝜑 ) → [ 𝑦 / 𝑥 ] 𝜑 )

Proof

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