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 ) )