Metamath Proof Explorer

Theorem frege40

Description: Anything implies pm2.18 . Proposition 40 of Frege1879 p. 46. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege40 
|- ( -. ph -> ( ( -. ps -> ps ) -> ps ) )

Proof

Step Hyp Ref Expression
1 frege39 
 |-  ( ( -. ps -> ps ) -> ( -. ps -> ph ) )
2 frege35 
 |-  ( ( ( -. ps -> ps ) -> ( -. ps -> ph ) ) -> ( -. ph -> ( ( -. ps -> ps ) -> ps ) ) )
3 1 2 ax-mp 
 |-  ( -. ph -> ( ( -. ps -> ps ) -> ps ) )