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	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	cbvriotavw	$$⊢\left(\iota x\in A|\phi \right)=\left(\iota y\in A|\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		cbvriotavw.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
2		nfv	$$⊢Ⅎy\phi$$
3		nfv	$$⊢Ⅎx\psi$$
4	2 3 1	cbvriotaw	$$⊢\left(\iota x\in A|\phi \right)=\left(\iota y\in A|\psi \right)$$