Theorem cbvriotavw

Description: Change bound variable in a restricted description binder. Version of cbvriotav with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 18-Mar-2013) (Revised by Gino Giotto, 26-Jan-2024)

	Ref	Expression
Hypothesis	cbvriotavw.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
Assertion	cbvriotavw	⊢ ( ℩ 𝑥 ∈ 𝐴 𝜑 ) = ( ℩ 𝑦 ∈ 𝐴 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		cbvriotavw.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
2		nfv	⊢ Ⅎ 𝑦 𝜑
3		nfv	⊢ Ⅎ 𝑥 𝜓
4	2 3 1	cbvriotaw	⊢ ( ℩ 𝑥 ∈ 𝐴 𝜑 ) = ( ℩ 𝑦 ∈ 𝐴 𝜓 )