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Theorem frege22 38113
Description: A closed form of com45 97. Proposition 22 of [Frege1879] p. 41. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege22 |- ( ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) ) -> ( ph -> ( ps -> ( ch -> ( ta -> ( th -> et ) ) ) ) ) )
Proof of Theorem frege22
StepHypRef Expression
1 frege16 38110 . 2 |- ( ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) -> ( ps -> ( ch -> ( ta -> ( th -> et ) ) ) ) )
2 frege5 38094 . 2 |- ( ( ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) -> ( ps -> ( ch -> ( ta -> ( th -> et ) ) ) ) ) -> ( ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) ) -> ( ph -> ( ps -> ( ch -> ( ta -> ( th -> et ) ) ) ) ) ) )
31, 2ax-mp 5 1 |- ( ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) ) -> ( ph -> ( ps -> ( ch -> ( ta -> ( th -> et ) ) ) ) ) )
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:  frege23  38119
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