Description: Inference associated with simprim . Proved exactly as step 11 is obtained from step 4 in dfbi1ALTa . (Contributed by Eric Schmidt, 22-Oct-2025) (New usage is discouraged.) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | simprimi.1 | |- -. ( ph -> -. ps ) |
|
| Assertion | simprimi | |- ps |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simprimi.1 | |- -. ( ph -> -. ps ) |
|
| 2 | tru | |- T. |
|
| 3 | ax-1 | |- ( -. ps -> ( ph -> -. ps ) ) |
|
| 4 | 1 | a1i | |- ( -. -. T. -> -. ( ph -> -. ps ) ) |
| 5 | 4 | con4i | |- ( ( ph -> -. ps ) -> -. T. ) |
| 6 | 5 | a1i | |- ( -. ps -> ( ( ph -> -. ps ) -> -. T. ) ) |
| 7 | 6 | a2i | |- ( ( -. ps -> ( ph -> -. ps ) ) -> ( -. ps -> -. T. ) ) |
| 8 | 3 7 | ax-mp | |- ( -. ps -> -. T. ) |
| 9 | 8 | con4i | |- ( T. -> ps ) |
| 10 | 2 9 | ax-mp | |- ps |