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

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

Proof

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