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Metamath Proof Explorer

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 → ( 𝜑 ↔ 𝜓 ) )
	Assertion	cbvriotav	⊢ ( ℩ 𝑥 ∈ 𝐴 𝜑 ) = ( ℩ 𝑦 ∈ 𝐴 𝜓 )

Proof

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