Theorem sbciegOLD

Description: Obsolete version of sbcieg as of 12-Oct-2024. (Contributed by NM, 10-Nov-2005) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	sbciegOLD.1	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
Assertion	sbciegOLD	⊢ ( 𝐴 ∈ 𝑉 → ( [ 𝐴 / 𝑥 ] 𝜑 ↔ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		sbciegOLD.1	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
2		nfv	⊢ Ⅎ 𝑥 𝜓
3	2 1	sbciegf	⊢ ( 𝐴 ∈ 𝑉 → ( [ 𝐴 / 𝑥 ] 𝜑 ↔ 𝜓 ) )