Description: Rederivation of ax-c11n from original version ax-c11 . See Theorem axc11 for the derivation of ax-c11 from ax-c11n .
This theorem should not be referenced in any proof. Instead, use ax-c11n above so that uses of ax-c11n can be more easily identified, or use aecom-o when this form is needed for studies involving ax-c11 and omitting ax-5 . (Contributed by NM, 16-May-2008) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | axc11nfromc11 | |- ( A. x x = y -> A. y y = x ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-c11 | |- ( 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 | 3 | alimi | |- ( A. y x = y -> A. y y = x ) |
| 5 | 2 4 | syl | |- ( A. x x = y -> A. y y = x ) |