Metamath Proof Explorer

Theorem frege30

Description: Commuted, closed form of con3d . Proposition 30 of Frege1879 p. 44. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege30 
|- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( -. ch -> -. ph ) ) )

Proof

Step Hyp Ref Expression
1 frege29 
 |-  ( ( ps -> ( ph -> ch ) ) -> ( ps -> ( -. ch -> -. ph ) ) )
2 frege10 
 |-  ( ( ( ps -> ( ph -> ch ) ) -> ( ps -> ( -. ch -> -. ph ) ) ) -> ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( -. ch -> -. ph ) ) ) )
3 1 2 ax-mp 
 |-  ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( -. ch -> -. ph ) ) )