Metamath Proof Explorer


Theorem frege39

Description: Syllogism between pm2.18 and pm2.24 . Proposition 39 of Frege1879 p. 46. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege39
|- ( ( -. ph -> ph ) -> ( -. ph -> ps ) )

Proof

Step Hyp Ref Expression
1 frege38
 |-  ( -. ph -> ( ph -> ps ) )
2 ax-frege2
 |-  ( ( -. ph -> ( ph -> ps ) ) -> ( ( -. ph -> ph ) -> ( -. ph -> ps ) ) )
3 1 2 ax-mp
 |-  ( ( -. ph -> ph ) -> ( -. ph -> ps ) )