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Theorem frege14 38117
Description: Closed form of a deduction based on com3r 87. Proposition 14 of [Frege1879] p. 37. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege14 |- ( ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) ) -> ( ph -> ( th -> ( ps -> ( ch -> ta ) ) ) ) )
Proof of Theorem frege14
StepHypRef Expression
1 frege13 38116 . 2 |- ( ( ps -> ( ch -> ( th -> ta ) ) ) -> ( th -> ( ps -> ( ch -> ta ) ) ) )
2 frege5 38094 . 2 |- ( ( ( ps -> ( ch -> ( th -> ta ) ) ) -> ( th -> ( ps -> ( ch -> ta ) ) ) ) -> ( ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) ) -> ( ph -> ( th -> ( ps -> ( ch -> ta ) ) ) ) ) )
31, 2ax-mp 5 1 |- ( ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) ) -> ( ph -> ( th -> ( ps -> ( ch -> ta ) ) ) ) )
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:  frege15  38120
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