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Theorem frege12 38609
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 38605 . 2 ((𝜓 → (𝜒𝜃)) → (𝜒 → (𝜓𝜃)))
2 frege5 38596 . 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 38586  ax-frege2 38587  ax-frege8 38605
This theorem is referenced by:  frege24  38611  frege16  38612  frege13  38618  frege15  38622  frege35  38634  frege49  38649  frege60a  38674  frege60b  38701  frege60c  38719  frege85  38744  frege127  38786
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