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Theorem frege44 38142
Description: Similar to a commuted pm2.62 425. Proposition 44 of [Frege1879] p. 47. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege44 |- ( ( -. ph -> ps ) -> ( ( ps -> ph ) -> ph ) )
Proof of Theorem frege44
StepHypRef Expression
1 frege43 38141 . 2 |- ( ( -. ph -> ph ) -> ph )
2 frege21 38121 . 2 |- ( ( ( -. ph -> ph ) -> ph ) -> ( ( -. ph -> ps ) -> ( ( ps -> ph ) -> ph ) ) )
31, 2ax-mp 5 1 |- ( ( -. ph -> ps ) -> ( ( ps -> ph ) -> 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  ax-frege31 38128  ax-frege41 38139
This theorem is referenced by:  frege45  38143
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