Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege30 Structured version   Visualization version   GIF version

Theorem frege30 36945
Description: Commuted, closed form of con3d 146. Proposition 30 of [Frege1879] p. 44. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege30 ((𝜑 → (𝜓𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑)))

Proof of Theorem frege30
StepHypRef Expression
1 frege29 36944 . 2 ((𝜓 → (𝜑𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑)))
2 frege10 36933 . 2 (((𝜓 → (𝜑𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑))) → ((𝜑 → (𝜓𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36903  ax-frege2 36904  ax-frege8 36922  ax-frege28 36943
This theorem is referenced by:  frege59a  36990  frege59b  37017  frege59c  37035
  Copyright terms: Public domain W3C validator