Metamath Proof Explorer


Theorem expt

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 ) ) )

Proof

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 ) ) )