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Theorem frege12 38424
Description: A closed form of com23 86. Proposition 12 of [Frege1879] p. 37. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege12 ((𝜑 → (𝜓 → (𝜒𝜃))) → (𝜑 → (𝜒 → (𝜓𝜃))))

Proof of Theorem frege12
StepHypRef Expression
1 ax-frege8 38420 . 2 ((𝜓 → (𝜒𝜃)) → (𝜒 → (𝜓𝜃)))
2 frege5 38411 . 2 (((𝜓 → (𝜒𝜃)) → (𝜒 → (𝜓𝜃))) → ((𝜑 → (𝜓 → (𝜒𝜃))) → (𝜑 → (𝜒 → (𝜓𝜃)))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓 → (𝜒𝜃))) → (𝜑 → (𝜒 → (𝜓𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 38401  ax-frege2 38402  ax-frege8 38420
This theorem is referenced by:  frege24  38426  frege16  38427  frege13  38433  frege15  38437  frege35  38449  frege49  38464  frege60a  38489  frege60b  38516  frege60c  38534  frege85  38559  frege127  38601
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