Metamath Proof Explorer


Theorem bj-nfsab1

Description: Remove dependency on ax-13 from nfsab1 . UPDATE / TODO: nfsab1 does not use ax-13 either anymore; bj-nfsab1 is shorter than nfsab1 but uses ax-12 . (Contributed by BJ, 23-Jun-2019) (Proof modification is discouraged.)

Ref Expression
Assertion bj-nfsab1 𝑥 𝑦 ∈ { 𝑥𝜑 }

Proof

Step Hyp Ref Expression
1 hbab1 ( 𝑦 ∈ { 𝑥𝜑 } → ∀ 𝑥 𝑦 ∈ { 𝑥𝜑 } )
2 1 nf5i 𝑥 𝑦 ∈ { 𝑥𝜑 }