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Metamath Proof Explorer

Theorem nfriota1

Description: The abstraction variable in a restricted iota descriptor isn't free. (Contributed by NM, 12-Oct-2011) (Revised by Mario Carneiro, 15-Oct-2016)

		Ref	Expression
	Assertion	nfriota1	⊢ Ⅎ 𝑥 ( ℩ 𝑥 ∈ 𝐴 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		df-riota	⊢ ( ℩ 𝑥 ∈ 𝐴 𝜑 ) = ( ℩ 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) )
2		nfiota1	⊢ Ⅎ 𝑥 ( ℩ 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) )
3	1 2	nfcxfr	⊢ Ⅎ 𝑥 ( ℩ 𝑥 ∈ 𝐴 𝜑 )