Description: Closed form of syl with swapped antecedents. This proposition differs from frege5 only in an unessential way. Identical to imim1 . Proposition 9 of Frege1879 p. 35. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | frege9 | |- ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | frege5 | |- ( ( ps -> ch ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) ) |
|
| 2 | ax-frege8 | |- ( ( ( ps -> ch ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) ) -> ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) ) |