Description: If ch is a necessary consequence of the occurrence of ps or ph , then ch is a necessary consequence of ph alone. Similar to a closed form of orcs . Proposition 37 of Frege1879 p. 46. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | frege37 | |- ( ( ( -. ph -> ps ) -> ch ) -> ( ph -> ch ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | frege36 | |- ( ph -> ( -. ph -> ps ) ) |
|
| 2 | frege9 | |- ( ( ph -> ( -. ph -> ps ) ) -> ( ( ( -. ph -> ps ) -> ch ) -> ( ph -> ch ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ( ( -. ph -> ps ) -> ch ) -> ( ph -> ch ) ) |