Theorem axc11n11

Description: Proof of axc11n from { ax-1 -- ax-7 , axc11 } . Almost identical to axc11nfromc11 . (Contributed by NM, 6-Jul-2021) (Proof modification is discouraged.)

	Ref	Expression
Assertion	axc11n11	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑦 𝑦 = 𝑥 )

Proof

Step	Hyp	Ref	Expression
1		axc11	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ( ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑦 𝑥 = 𝑦 ) )
2	1	pm2.43i	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑦 𝑥 = 𝑦 )
3		equcomi	⊢ ( 𝑥 = 𝑦 → 𝑦 = 𝑥 )
4	2 3	sylg	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑦 𝑦 = 𝑥 )