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Theorem frege25 38111
Description: Closed form for a1dd 50. Proposition 25 of [Frege1879] p. 42. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege25 |- ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ps -> ( th -> ch ) ) ) )
Proof of Theorem frege25
StepHypRef Expression
1 frege24 38109 . 2 |- ( ( ps -> ch ) -> ( ps -> ( th -> ch ) ) )
2 frege5 38094 . 2 |- ( ( ( ps -> ch ) -> ( ps -> ( th -> ch ) ) ) -> ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ps -> ( th -> ch ) ) ) ) )
31, 2ax-mp 5 1 |- ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ps -> ( th -> ch ) ) ) )
Colors of variables: wff setvar class
Syntax hints:   -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085  ax-frege8 38103
This theorem is referenced by:  frege111  38268
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