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Theorem frege15 36938
Description: A closed form of com4r 91. Proposition 15 of [Frege1879] p. 38. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege15 ((𝜑 → (𝜓 → (𝜒 → (𝜃𝜏)))) → (𝜃 → (𝜑 → (𝜓 → (𝜒𝜏)))))

Proof of Theorem frege15
StepHypRef Expression
1 frege14 36935 . 2 ((𝜑 → (𝜓 → (𝜒 → (𝜃𝜏)))) → (𝜑 → (𝜃 → (𝜓 → (𝜒𝜏)))))
2 frege12 36925 . 2 (((𝜑 → (𝜓 → (𝜒 → (𝜃𝜏)))) → (𝜑 → (𝜃 → (𝜓 → (𝜒𝜏))))) → ((𝜑 → (𝜓 → (𝜒 → (𝜃𝜏)))) → (𝜃 → (𝜑 → (𝜓 → (𝜒𝜏))))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓 → (𝜒 → (𝜃𝜏)))) → (𝜃 → (𝜑 → (𝜓 → (𝜒𝜏)))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36902  ax-frege2 36903  ax-frege8 36921
This theorem is referenced by:  frege88  37063
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