MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.51 Structured version   Visualization version   GIF version

Theorem pm2.51 165
Description: Theorem *2.51 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.51 (¬ (𝜑𝜓) → (𝜑 → ¬ 𝜓))

Proof of Theorem pm2.51
StepHypRef Expression
1 ax-1 6 . . 3 (𝜓 → (𝜑𝜓))
21con3i 150 . 2 (¬ (𝜑𝜓) → ¬ 𝜓)
32a1d 25 1 (¬ (𝜑𝜓) → (𝜑 → ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  pm5.12  928
  Copyright terms: Public domain W3C validator