Description: Standard propositional axiom derived from Lukasiewicz axioms. (Contributed by NM, 22-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ax3 | |- ( ( -. ph -> -. ps ) -> ( ps -> ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | luklem2 | |- ( ( -. ph -> -. ps ) -> ( ( ( -. ph -> ph ) -> ph ) -> ( ps -> ph ) ) ) |
|
| 2 | luklem4 | |- ( ( ( ( -. ph -> ph ) -> ph ) -> ( ps -> ph ) ) -> ( ps -> ph ) ) |
|
| 3 | 1 2 | luklem1 | |- ( ( -. ph -> -. ps ) -> ( ps -> ph ) ) |