Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege14 Structured version   Visualization version   GIF version

Theorem frege14 38815
Description: Closed form of a deduction based on com3r 87. Proposition 14 of [Frege1879] p. 37. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege14 ((𝜑 → (𝜓 → (𝜒 → (𝜃𝜏)))) → (𝜑 → (𝜃 → (𝜓 → (𝜒𝜏)))))

Proof of Theorem frege14
StepHypRef Expression
1 frege13 38814 . 2 ((𝜓 → (𝜒 → (𝜃𝜏))) → (𝜃 → (𝜓 → (𝜒𝜏))))
2 frege5 38792 . 2 (((𝜓 → (𝜒 → (𝜃𝜏))) → (𝜃 → (𝜓 → (𝜒𝜏)))) → ((𝜑 → (𝜓 → (𝜒 → (𝜃𝜏)))) → (𝜑 → (𝜃 → (𝜓 → (𝜒𝜏))))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓 → (𝜒 → (𝜃𝜏)))) → (𝜑 → (𝜃 → (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:  frege15  38818
  Copyright terms: Public domain W3C validator