Theorem cbviotavw

Description: Change bound variables in a description binder. Version of cbviotav with a disjoint variable condition, which does not require ax-13 . (Contributed by Andrew Salmon, 1-Aug-2011) (Revised by Gino Giotto, 26-Jan-2024)

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

Proof

Step	Hyp	Ref	Expression
1		cbviotavw.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
2		nfv	⊢ Ⅎ 𝑦 𝜑
3		nfv	⊢ Ⅎ 𝑥 𝜓
4	1 2 3	cbviotaw	⊢ ( ℩ 𝑥 𝜑 ) = ( ℩ 𝑦 𝜓 )