Metamath Proof Explorer


Theorem exptOLD

Description: Obsolete version of expt as of 25-May-2026. Exportation theorem pm3.3 (closed form of ex ) expressed with primitive connectives. (Contributed by NM, 28-Dec-1992) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion exptOLD
|- ( ( -. ( ph -> -. ps ) -> ch ) -> ( ph -> ( ps -> ch ) ) )

Proof

Step Hyp Ref Expression
1 pm3.2im
 |-  ( ph -> ( ps -> -. ( ph -> -. ps ) ) )
2 1 imim1d
 |-  ( ph -> ( ( -. ( ph -> -. ps ) -> ch ) -> ( ps -> ch ) ) )
3 2 com12
 |-  ( ( -. ( ph -> -. ps ) -> ch ) -> ( ph -> ( ps -> ch ) ) )