Theorem nfiota

Description: Bound-variable hypothesis builder for the iota class. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfiotaw when possible. (Contributed by NM, 23-Aug-2011) (New usage is discouraged.)

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

Proof

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