Description: Second lemma for the derivation of ax-1 and ax-2 from adh-minim and ax-mp . Polish prefix notation: CCpCCqCCrCpsCrstCpt . (Contributed by ADH, 10-Nov-2023) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | adh-minim-ax1-ax2-lem2 | |- ( ( ph -> ( ( ps -> ( ( ch -> ( ph -> th ) ) -> ( ch -> th ) ) ) -> ta ) ) -> ( ph -> ta ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | adh-minim-ax1-ax2-lem1 | |- ( et -> ( ( ze -> ( ( si -> ( ( rh -> ( ze -> mu ) ) -> ( rh -> mu ) ) ) -> la ) ) -> ( ze -> la ) ) ) |
|
| 2 | adh-minim-ax1-ax2-lem1 | |- ( ( et -> ( ( ze -> ( ( si -> ( ( rh -> ( ze -> mu ) ) -> ( rh -> mu ) ) ) -> la ) ) -> ( ze -> la ) ) ) -> ( ( ph -> ( ( ps -> ( ( ch -> ( ph -> th ) ) -> ( ch -> th ) ) ) -> ta ) ) -> ( ph -> ta ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ( ph -> ( ( ps -> ( ( ch -> ( ph -> th ) ) -> ( ch -> th ) ) ) -> ta ) ) -> ( ph -> ta ) ) |