MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm4.64 Structured version   Visualization version   GIF version

Theorem pm4.64 385
Description: Theorem *4.64 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.64 ((¬ 𝜑𝜓) ↔ (𝜑𝜓))

Proof of Theorem pm4.64
StepHypRef Expression
1 df-or 383 . 2 ((𝜑𝜓) ↔ (¬ 𝜑𝜓))
21bicomi 212 1 ((¬ 𝜑𝜓) ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 194  wo 381
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 195  df-or 383
This theorem is referenced by:  pm4.66  434  ioran  509  dfifp3  1008  dfnf5  3905  fimaxg  8069  fiming  8264  kmlem8  8839  axgroth6  9506  dfcon2  20979  ifpimimb  36651  ifpor123g  36655  hirstL-ax3  39491
  Copyright terms: Public domain W3C validator