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Theorem frege22 40155
Description: A closed form of com45 97. Proposition 22 of [Frege1879] p. 41. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege22 ((𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂))))) → (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜃𝜂))))))

Proof of Theorem frege22
StepHypRef Expression
1 frege16 40152 . 2 ((𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))) → (𝜓 → (𝜒 → (𝜏 → (𝜃𝜂)))))
2 frege5 40136 . 2 (((𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))) → (𝜓 → (𝜒 → (𝜏 → (𝜃𝜂))))) → ((𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂))))) → (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜃𝜂)))))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂))))) → (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜃𝜂))))))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 40126  ax-frege2 40127  ax-frege8 40145
This theorem is referenced by:  frege23  40161
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