Description: Exportation theorem pm3.3 (closed form of ex ) expressed with primitive connectives. (Contributed by NM, 28-Dec-1992) (Proof shortened by Garrett Katz, 25-May-2026)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | expt | |- ( ( -. ( ph -> -. ps ) -> ch ) -> ( ph -> ( ps -> ch ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm3.2im | |- ( ph -> ( ps -> -. ( ph -> -. ps ) ) ) |
|
| 2 | id | |- ( ( -. ( ph -> -. ps ) -> ch ) -> ( -. ( ph -> -. ps ) -> ch ) ) |
|
| 3 | 1 2 | syl9r | |- ( ( -. ( ph -> -. ps ) -> ch ) -> ( ph -> ( ps -> ch ) ) ) |