Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege29 Structured version   Visualization version   Unicode version
Theorem frege29 38125
Description: Closed form of con3d 148. Proposition 29 of [Frege1879] p. 43. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege29 |- ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( -. ch -> -. ps ) ) )
Proof of Theorem frege29
StepHypRef Expression
1 ax-frege28 38124 . 2 |- ( ( ps -> ch ) -> ( -. ch -> -. ps ) )
2 frege5 38094 . 2 |- ( ( ( ps -> ch ) -> ( -. ch -> -. ps ) ) -> ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( -. ch -> -. ps ) ) ) )
31, 2ax-mp 5 1 |- ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( -. ch -> -. 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-frege28 38124
This theorem is referenced by:  frege30  38126
  Copyright terms: Public domain W3C validator