MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm4.8 Structured version   Visualization version   GIF version

Theorem pm4.8 379
Description: Theorem *4.8 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.8 ((𝜑 → ¬ 𝜑) ↔ ¬ 𝜑)

Proof of Theorem pm4.8
StepHypRef Expression
1 pm2.01 179 . 2 ((𝜑 → ¬ 𝜑) → ¬ 𝜑)
2 ax-1 6 . 2 𝜑 → (𝜑 → ¬ 𝜑))
31, 2impbii 198 1 ((𝜑 → ¬ 𝜑) ↔ ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 195
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 196
This theorem is referenced by:  wl-nannot  32478  ifpimimb  36868
  Copyright terms: Public domain W3C validator