Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege39 Structured version   Visualization version   GIF version

Theorem frege39 40323
Description: Syllogism between pm2.18 128 and pm2.24 124. Proposition 39 of [Frege1879] p. 46. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege39 ((¬ 𝜑𝜑) → (¬ 𝜑𝜓))

Proof of Theorem frege39
StepHypRef Expression
1 frege38 40322 . 2 𝜑 → (𝜑𝜓))
2 ax-frege2 40272 . 2 ((¬ 𝜑 → (𝜑𝜓)) → ((¬ 𝜑𝜑) → (¬ 𝜑𝜓)))
31, 2ax-mp 5 1 ((¬ 𝜑𝜑) → (¬ 𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 40271  ax-frege2 40272  ax-frege8 40290  ax-frege28 40311  ax-frege31 40315
This theorem is referenced by:  frege40  40324
  Copyright terms: Public domain W3C validator