Description: Derivation of ax-1 from adh-minimp and ax-mp . Polish prefix notation: CpCqp . (Contributed by BJ, 4-Apr-2021) (Revised by ADH, 10-Nov-2023) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | adh-minimp-ax1 | |- ( ph -> ( ps -> ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | adh-minimp-sylsimp | |- ( ( ( ph -> ps ) -> ph ) -> ( ps -> ph ) ) |
|
| 2 | adh-minimp-sylsimp | |- ( ( ( ( ph -> ps ) -> ph ) -> ( ps -> ph ) ) -> ( ph -> ( ps -> ph ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ph -> ( ps -> ph ) ) |