Description: 3 of 3 axioms for propositional calculus due to Lukasiewicz, derived from Meredith's sole axiom. (Contributed by NM, 14-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | luk-3 | |- ( ph -> ( -. ph -> ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | merlem11 | |- ( ( -. ph -> ( -. ph -> ps ) ) -> ( -. ph -> ps ) ) |
|
| 2 | merlem1 | |- ( ( ( -. ph -> ( -. ph -> ps ) ) -> ( -. ph -> ps ) ) -> ( ph -> ( -. ph -> ps ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( ph -> ( -. ph -> ps ) ) |