Metamath Proof Explorer

Theorem frege35

Description: Commuted, closed form of con1d . Proposition 35 of Frege1879 p. 45. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege35 
|- ( ( ph -> ( -. ps -> ch ) ) -> ( -. ch -> ( ph -> ps ) ) )

Proof

Step Hyp Ref Expression
1 frege34 
 |-  ( ( ph -> ( -. ps -> ch ) ) -> ( ph -> ( -. ch -> ps ) ) )
2 frege12 
 |-  ( ( ( ph -> ( -. ps -> ch ) ) -> ( ph -> ( -. ch -> ps ) ) ) -> ( ( ph -> ( -. ps -> ch ) ) -> ( -. ch -> ( ph -> ps ) ) ) )
3 1 2 ax-mp 
 |-  ( ( ph -> ( -. ps -> ch ) ) -> ( -. ch -> ( ph -> ps ) ) )