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Metamath Proof Explorer

Theorem cbviotav

Description: Change bound variables in a description binder. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbviotavw when possible. (Contributed by Andrew Salmon, 1-Aug-2011) (New usage is discouraged.)

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

Proof

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