Metamath Proof Explorer


Theorem axc16nfALT

Description: Alternate proof of axc16nf , shorter but requiring ax-11 and ax-13 . (Contributed by Mario Carneiro, 7-Oct-2016) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion axc16nfALT ⊢ ∀ x x = y → Ⅎ z φ

Proof

Step Hyp Ref Expression
1 nfae ⊢ Ⅎ z ∀ x x = y
2 axc16g ⊢ ∀ x x = y → φ → ∀ z φ
3 1 2 nf5d ⊢ ∀ x x = y → Ⅎ z φ