Theorem cbvrabvOLD

Description: Obsolete version of cbvrabv as of 14-Jun-2023. Rule to change the bound variable in a restricted class abstraction, using implicit substitution. (Contributed by NM, 26-May-1999) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	cbvrabvOLD.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
Assertion	cbvrabvOLD	⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } = { 𝑦 ∈ 𝐴 ∣ 𝜓 }

Proof

Step	Hyp	Ref	Expression
1		cbvrabvOLD.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
2		nfcv	⊢ Ⅎ 𝑥 𝐴
3		nfcv	⊢ Ⅎ 𝑦 𝐴
4		nfv	⊢ Ⅎ 𝑦 𝜑
5		nfv	⊢ Ⅎ 𝑥 𝜓
6	2 3 4 5 1	cbvrab	⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } = { 𝑦 ∈ 𝐴 ∣ 𝜓 }