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Theorem frege12 40445
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 40441 . 2 ((𝜓 → (𝜒𝜃)) → (𝜒 → (𝜓𝜃)))
2 frege5 40432 . 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 40422  ax-frege2 40423  ax-frege8 40441
This theorem is referenced by:  frege24  40447  frege16  40448  frege13  40454  frege15  40458  frege35  40470  frege49  40485  frege60a  40510  frege60b  40537  frege60c  40555  frege85  40580  frege127  40622
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