Metamath Proof Explorer


Theorem bj-axc16g16

Description: Proof of axc16g from { ax-1 -- ax-7 , axc16 }. (Contributed by BJ, 6-Jul-2021) (Proof modification is discouraged.)

Ref Expression
Assertion bj-axc16g16 ⊢ ∀ x x = y → φ → ∀ z φ

Proof

Step Hyp Ref Expression
1 aevlem ⊢ ∀ x x = y → ∀ z z = t
2 axc16 ⊢ ∀ z z = t → φ → ∀ z φ
3 1 2 syl ⊢ ∀ x x = y → φ → ∀ z φ