Theorem sbcbi2OLD

Description: Obsolete proof of sbcbi2 as of 5-May-2024. (Contributed by Giovanni Mascellani, 9-Apr-2018) (Proof shortened by Wolf Lammen, 4-May-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	sbcbi2OLD	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( [ 𝐴 / 𝑥 ] 𝜑 ↔ [ 𝐴 / 𝑥 ] 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		nfa1	⊢ Ⅎ 𝑥 ∀ 𝑥 ( 𝜑 ↔ 𝜓 )
2		sp	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )
3	1 2	sbcbid	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( [ 𝐴 / 𝑥 ] 𝜑 ↔ [ 𝐴 / 𝑥 ] 𝜓 ) )