Description: Proof of a single axiom that can replace ax-c5 and ax-c7 . See axc5c7toc5 and axc5c7toc7 for the rederivation of those axioms. (Contributed by Scott Fenton, 12-Sep-2005) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | axc5c7 | |- ( ( A. x -. A. x ph -> A. x ph ) -> ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-c7 | |- ( -. A. x -. A. x ph -> ph ) |
|
| 2 | ax-c5 | |- ( A. x ph -> ph ) |
|
| 3 | 1 2 | ja | |- ( ( A. x -. A. x ph -> A. x ph ) -> ph ) |