Description: Fourth lemma for the derivation of ax-1 and ax-2 from adh-minim and ax-mp . Polish prefix notation: CCCpqrCCqCrsCqs . (Contributed by ADH, 10-Nov-2023) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | adh-minim-ax1-ax2-lem4 | |- ( ( ( ph -> ps ) -> ch ) -> ( ( ps -> ( ch -> th ) ) -> ( ps -> th ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | adh-minim | |- ( ( ( ph -> ps ) -> ch ) -> ( ( et -> ( ( ze -> ( ( ( ph -> ps ) -> ch ) -> si ) ) -> ( ze -> si ) ) ) -> ( ( ps -> ( ch -> th ) ) -> ( ps -> th ) ) ) ) |
|
| 2 | adh-minim-ax1-ax2-lem2 | |- ( ( ( ( ph -> ps ) -> ch ) -> ( ( et -> ( ( ze -> ( ( ( ph -> ps ) -> ch ) -> si ) ) -> ( ze -> si ) ) ) -> ( ( ps -> ( ch -> th ) ) -> ( ps -> th ) ) ) ) -> ( ( ( ph -> ps ) -> ch ) -> ( ( ps -> ( ch -> th ) ) -> ( ps -> th ) ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ( ( ph -> ps ) -> ch ) -> ( ( ps -> ( ch -> th ) ) -> ( ps -> th ) ) ) |