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Theorem frege30 38126
Description: Commuted, closed form of con3d 148. Proposition 30 of [Frege1879] p. 44. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege30 |- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( -. ch -> -. ph ) ) )
Proof of Theorem frege30
StepHypRef Expression
1 frege29 38125 . 2 |- ( ( ps -> ( ph -> ch ) ) -> ( ps -> ( -. ch -> -. ph ) ) )
2 frege10 38114 . 2 |- ( ( ( ps -> ( ph -> ch ) ) -> ( ps -> ( -. ch -> -. ph ) ) ) -> ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( -. ch -> -. ph ) ) ) )
31, 2ax-mp 5 1 |- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( -. ch -> -. 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-frege8 38103  ax-frege28 38124
This theorem is referenced by:  frege59a  38171  frege59b  38198  frege59c  38216
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