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Theorem frege17 36934
Description: A closed form of com3l 86. Proposition 17 of [Frege1879] p. 39. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege17 ((𝜑 → (𝜓 → (𝜒𝜃))) → (𝜓 → (𝜒 → (𝜑𝜃))))

Proof of Theorem frege17
StepHypRef Expression
1 ax-frege8 36922 . 2 ((𝜑 → (𝜓 → (𝜒𝜃))) → (𝜓 → (𝜑 → (𝜒𝜃))))
2 frege16 36929 . 2 (((𝜑 → (𝜓 → (𝜒𝜃))) → (𝜓 → (𝜑 → (𝜒𝜃)))) → ((𝜑 → (𝜓 → (𝜒𝜃))) → (𝜓 → (𝜒 → (𝜑𝜃)))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓 → (𝜒𝜃))) → (𝜓 → (𝜒 → (𝜑𝜃))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36903  ax-frege2 36904  ax-frege8 36922
This theorem is referenced by:  frege50  36967  frege78  37054
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