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Theorem frege23 38119
Description: Syllogism followed by rotation of three antecedents. Proposition 23 of [Frege1879] p. 42. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege23 |- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ( ta -> ph ) -> ( ps -> ( ch -> ( ta -> th ) ) ) ) )
Proof of Theorem frege23
StepHypRef Expression
1 frege18 38112 . 2 |- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ( ta -> ph ) -> ( ps -> ( ta -> ( ch -> th ) ) ) ) )
2 frege22 38113 . 2 |- ( ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ( ta -> ph ) -> ( ps -> ( ta -> ( ch -> th ) ) ) ) ) -> ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ( ta -> ph ) -> ( ps -> ( ch -> ( ta -> th ) ) ) ) ) )
31, 2ax-mp 5 1 |- ( ( ph -> ( ps -> ( ch -> th ) ) ) -> ( ( ta -> ph ) -> ( ps -> ( ch -> ( ta -> th ) ) ) ) )
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:  frege48  38146
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