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	$$⊢\forall xx=y\to \forall yy=x$$

Proof

Step	Hyp	Ref	Expression
1		axc11	$$⊢\forall xx=y\to \left(\forall xx=y\to \forall yx=y\right)$$
2	1	pm2.43i	$$⊢\forall xx=y\to \forall yx=y$$
3		equcomi	$$⊢x=y\to y=x$$
4	2 3	sylg	$$⊢\forall xx=y\to \forall yy=x$$