Description: If ph or ps takes place, then ps or ph takes place. Identical to con1 . Proposition 33 of Frege1879 p. 44. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | frege33 | |- ( ( -. ph -> ps ) -> ( -. ps -> ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-frege28 | |- ( ( -. ph -> ps ) -> ( -. ps -> -. -. ph ) ) |
|
| 2 | frege32 | |- ( ( ( -. ph -> ps ) -> ( -. ps -> -. -. ph ) ) -> ( ( -. ph -> ps ) -> ( -. ps -> ph ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ( -. ph -> ps ) -> ( -. ps -> ph ) ) |