Theorem cbvriotav

Description: Change bound variable in a restricted description binder. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbvriotavw when possible. (Contributed by NM, 18-Mar-2013) (Revised by Mario Carneiro, 15-Oct-2016) (New usage is discouraged.)

	Ref	Expression
Hypothesis	cbvriotav.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	cbvriotav	$$⊢\left(\iota x\in A|\phi \right)=\left(\iota y\in A|\psi \right)$$

Proof

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