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Theorem frege32 38129
Description: Deduce con1 143 from con3 149. Proposition 32 of [Frege1879] p. 44. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege32 |- ( ( ( -. ph -> ps ) -> ( -. ps -> -. -. ph ) ) -> ( ( -. ph -> ps ) -> ( -. ps -> ph ) ) )
Proof of Theorem frege32
StepHypRef Expression
1 ax-frege31 38128 . 2 |- ( -. -. ph -> ph )
2 frege7 38102 . 2 |- ( ( -. -. ph -> ph ) -> ( ( ( -. ph -> ps ) -> ( -. ps -> -. -. ph ) ) -> ( ( -. ph -> ps ) -> ( -. ps -> ph ) ) ) )
31, 2ax-mp 5 1 |- ( ( ( -. ph -> ps ) -> ( -. ps -> -. -. ph ) ) -> ( ( -. ph -> ps ) -> ( -. ps -> ph ) ) )
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-frege31 38128
This theorem is referenced by:  frege33  38130
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