Description: Sixth lemma for the derivation of ax-2 from adh-minim and ax-mp . Polish prefix notation: CCpCCCCqrsCCrCstCrtuCpu . (Contributed by ADH, 10-Nov-2023) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | adh-minim-ax2-lem6 | |- ( ( ph -> ( ( ( ( ps -> ch ) -> th ) -> ( ( ch -> ( th -> ta ) ) -> ( ch -> ta ) ) ) -> et ) ) -> ( ph -> et ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | adh-minim-ax2-lem5 | |- ( ( ze -> ph ) -> ( ( ( ps -> ch ) -> th ) -> ( ( ch -> ( th -> ta ) ) -> ( ch -> ta ) ) ) ) |
|
| 2 | adh-minim-ax1-ax2-lem4 | |- ( ( ( ze -> ph ) -> ( ( ( ps -> ch ) -> th ) -> ( ( ch -> ( th -> ta ) ) -> ( ch -> ta ) ) ) ) -> ( ( ph -> ( ( ( ( ps -> ch ) -> th ) -> ( ( ch -> ( th -> ta ) ) -> ( ch -> ta ) ) ) -> et ) ) -> ( ph -> et ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ( ph -> ( ( ( ( ps -> ch ) -> th ) -> ( ( ch -> ( th -> ta ) ) -> ( ch -> ta ) ) ) -> et ) ) -> ( ph -> et ) ) |