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Theorem frege12 43246
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 43242 . 2 ((𝜓 → (𝜒𝜃)) → (𝜒 → (𝜓𝜃)))
2 frege5 43233 . 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 43223  ax-frege2 43224  ax-frege8 43242
This theorem is referenced by:  frege24  43248  frege16  43249  frege13  43255  frege15  43259  frege35  43271  frege49  43286  frege60a  43311  frege60b  43338  frege60c  43356  frege85  43381  frege127  43423
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