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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	$⊢ \underline{Ⅎ} x (ι y \| φ)$

Proof

Step	Hyp	Ref	Expression
1		nfiotaw.1	$⊢ Ⅎ x φ$
2		nftru	$⊢ Ⅎ y ⊤$
3	1	a1i	$⊢ ⊤ \to Ⅎ x φ$
4	2 3	nfiotadw	$⊢ ⊤ \to \underline{Ⅎ} x (ι y \| φ)$
5	4	mptru	$⊢ \underline{Ⅎ} x (ι y \| φ)$