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Theorem frege35 38132
Description: Commuted, closed form of con1d 139. Proposition 35 of [Frege1879] p. 45. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege35 |- ( ( ph -> ( -. ps -> ch ) ) -> ( -. ch -> ( ph -> ps ) ) )
Proof of Theorem frege35
StepHypRef Expression
1 frege34 38131 . 2 |- ( ( ph -> ( -. ps -> ch ) ) -> ( ph -> ( -. ch -> ps ) ) )
2 frege12 38107 . 2 |- ( ( ( ph -> ( -. ps -> ch ) ) -> ( ph -> ( -. ch -> ps ) ) ) -> ( ( ph -> ( -. ps -> ch ) ) -> ( -. ch -> ( ph -> ps ) ) ) )
31, 2ax-mp 5 1 |- ( ( ph -> ( -. ps -> ch ) ) -> ( -. ch -> ( 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
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