Description: ax-3 proved from Lukasiewicz's axioms. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | wl-luk-ax3 | |- ( ( -. ph -> -. ps ) -> ( ps -> ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-luk3 | |- ( ps -> ( -. ps -> ph ) ) |
|
| 2 | ax-luk1 | |- ( ( -. ph -> -. ps ) -> ( ( -. ps -> ph ) -> ( -. ph -> ph ) ) ) |
|
| 3 | 1 2 | wl-luk-imtrid | |- ( ( -. ph -> -. ps ) -> ( ps -> ( -. ph -> ph ) ) ) |
| 4 | ax-luk2 | |- ( ( -. ph -> ph ) -> ph ) |
|
| 5 | 3 4 | wl-luk-imtrdi | |- ( ( -. ph -> -. ps ) -> ( ps -> ph ) ) |