Metamath Proof Explorer

Theorem frege44

Description: Similar to a commuted pm2.62 . Proposition 44 of Frege1879 p. 47. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege44 
|- ( ( -. ph -> ps ) -> ( ( ps -> ph ) -> ph ) )

Proof

Step Hyp Ref Expression
1 frege43 
 |-  ( ( -. ph -> ph ) -> ph )
2 frege21 
 |-  ( ( ( -. ph -> ph ) -> ph ) -> ( ( -. ph -> ps ) -> ( ( ps -> ph ) -> ph ) ) )
3 1 2 ax-mp 
 |-  ( ( -. ph -> ps ) -> ( ( ps -> ph ) -> ph ) )