Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege39 Structured version   Visualization version   Unicode version
Theorem frege39 38136
Description: Syllogism between pm2.18 122 and pm2.24 121. Proposition 39 of [Frege1879] p. 46. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege39 |- ( ( -. ph -> ph ) -> ( -. ph -> ps ) )
Proof of Theorem frege39
StepHypRef Expression
1 frege38 38135 . 2 |- ( -. ph -> ( ph -> ps ) )
2 ax-frege2 38085 . 2 |- ( ( -. ph -> ( ph -> ps ) ) -> ( ( -. ph -> ph ) -> ( -. ph -> ps ) ) )
31, 2ax-mp 5 1 |- ( ( -. ph -> ph ) -> ( -. ph -> ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085  ax-frege8 38103  ax-frege28 38124  ax-frege31 38128
This theorem is referenced by:  frege40  38137
  Copyright terms: Public domain W3C validator