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Theorem frege33 38130
Description: If ph or ps takes place, then ps or ph takes place. Identical to con1 143. Proposition 33 of [Frege1879] p. 44. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege33 |- ( ( -. ph -> ps ) -> ( -. ps -> ph ) )
Proof of Theorem frege33
StepHypRef Expression
1 ax-frege28 38124 . 2 |- ( ( -. ph -> ps ) -> ( -. ps -> -. -. ph ) )
2 frege32 38129 . 2 |- ( ( ( -. ph -> ps ) -> ( -. ps -> -. -. ph ) ) -> ( ( -. ph -> ps ) -> ( -. ps -> ph ) ) )
31, 2ax-mp 5 1 |- ( ( -. ph -> ps ) -> ( -. ps -> 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-frege28 38124  ax-frege31 38128
This theorem is referenced by:  frege34  38131  frege46  38144
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