Theorem sbcbidvOLD

Description: Obsolete version of sbcbidv as of 1-Dec-2023. (Contributed by NM, 29-Dec-2014) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	sbcbidv.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion	sbcbidvOLD	⊢ ( 𝜑 → ( [ 𝐴 / 𝑥 ] 𝜓 ↔ [ 𝐴 / 𝑥 ] 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		sbcbidv.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		nfv	⊢ Ⅎ 𝑥 𝜑
3	2 1	sbcbid	⊢ ( 𝜑 → ( [ 𝐴 / 𝑥 ] 𝜓 ↔ [ 𝐴 / 𝑥 ] 𝜒 ) )