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Theorem frege20 38820
Description: A closed form of syl8 76. Proposition 20 of [Frege1879] p. 40. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege20 ((𝜑 → (𝜓 → (𝜒𝜃))) → ((𝜃𝜏) → (𝜑 → (𝜓 → (𝜒𝜏)))))

Proof of Theorem frege20
StepHypRef Expression
1 frege19 38816 . 2 ((𝜓 → (𝜒𝜃)) → ((𝜃𝜏) → (𝜓 → (𝜒𝜏))))
2 frege18 38810 . 2 (((𝜓 → (𝜒𝜃)) → ((𝜃𝜏) → (𝜓 → (𝜒𝜏)))) → ((𝜑 → (𝜓 → (𝜒𝜃))) → ((𝜃𝜏) → (𝜑 → (𝜓 → (𝜒𝜏))))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓 → (𝜒𝜃))) → ((𝜃𝜏) → (𝜑 → (𝜓 → (𝜒𝜏)))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 38782  ax-frege2 38783  ax-frege8 38801
This theorem is referenced by:  frege121  38976  frege125  38980
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