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	⊢ Ⅎ 𝑥 𝜑
Assertion	nfiota	⊢ Ⅎ 𝑥 ( ℩ 𝑦 𝜑 )

Proof

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