Description: Rederivation of axc4 from axc5c4c711 . Note that only propositional calculus is required for the rederivation. (Contributed by Andrew Salmon, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | axc5c4c711toc4 | |- ( A. x ( A. x ph -> ps ) -> ( A. x ph -> A. x ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-1 | |- ( A. x ( A. x ph -> ps ) -> ( ph -> A. x ( A. x ph -> ps ) ) ) |
|
| 2 | ax-1 | |- ( ( ph -> A. x ( A. x ph -> ps ) ) -> ( A. x A. x -. A. x A. x ( A. x ph -> ps ) -> ( ph -> A. x ( A. x ph -> ps ) ) ) ) |
|
| 3 | axc5c4c711 | |- ( ( A. x A. x -. A. x A. x ( A. x ph -> ps ) -> ( ph -> A. x ( A. x ph -> ps ) ) ) -> ( A. x ph -> A. x ps ) ) |
|
| 4 | 1 2 3 | 3syl | |- ( A. x ( A. x ph -> ps ) -> ( A. x ph -> A. x ps ) ) |