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) (Revised by Gino Giotto, 26-Jan-2024)

	Ref	Expression
Hypothesis	nfiotaw.1	$$⊢Ⅎx\phi$$
Assertion	nfiotaw	$$⊢\underset{\_}{Ⅎ}x\left(\iota y|\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfiotaw.1	$$⊢Ⅎx\phi$$
2		nftru	$$⊢Ⅎy\top$$
3	1	a1i	$$⊢\top \to Ⅎx\phi$$
4	2 3	nfiotadw	$$⊢\top \to \underset{\_}{Ⅎ}x\left(\iota y|\phi \right)$$
5	4	mptru	$$⊢\underset{\_}{Ⅎ}x\left(\iota y|\phi \right)$$