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Metamath Proof Explorer

Theorem nfiotaw

Description: Bound-variable hypothesis builder for the iota class. Version of nfiota with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 23-Aug-2011) Avoid ax-13 . (Revised by GG, 26-Jan-2024)

		Ref	Expression
	Hypothesis	nfiotaw.1	⊢ Ⅎ 𝑥 𝜑
	Assertion	nfiotaw	⊢ Ⅎ 𝑥 ( ℩ 𝑦 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		nfiotaw.1	⊢ Ⅎ 𝑥 𝜑
2		nftru	⊢ Ⅎ 𝑦 ⊤
3	1	a1i	⊢ ( ⊤ → Ⅎ 𝑥 𝜑 )
4	2 3	nfiotadw	⊢ ( ⊤ → Ⅎ 𝑥 ( ℩ 𝑦 𝜑 ) )
5	4	mptru	⊢ Ⅎ 𝑥 ( ℩ 𝑦 𝜑 )