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 | |- ( A. x x = y -> A. y y = x ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | axc11 | |- ( A. x x = y -> ( A. x x = y -> A. y x = y ) ) |
|
| 2 | 1 | pm2.43i | |- ( A. x x = y -> A. y x = y ) |
| 3 | equcomi | |- ( x = y -> y = x ) |
|
| 4 | 2 3 | sylg | |- ( A. x x = y -> A. y y = x ) |