MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm4.55 Structured version   Visualization version   GIF version

Theorem pm4.55 513
Description: Theorem *4.55 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.55 (¬ (¬ 𝜑𝜓) ↔ (𝜑 ∨ ¬ 𝜓))

Proof of Theorem pm4.55
StepHypRef Expression
1 pm4.54 512 . . 3 ((¬ 𝜑𝜓) ↔ ¬ (𝜑 ∨ ¬ 𝜓))
21con2bii 345 . 2 ((𝜑 ∨ ¬ 𝜓) ↔ ¬ (¬ 𝜑𝜓))
32bicomi 212 1 (¬ (¬ 𝜑𝜓) ↔ (𝜑 ∨ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 194  wo 381  wa 382
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  df-an 384
This theorem is referenced by:  chrelat2i  28414  hlrelat2  33510  ifpnot23  36645
  Copyright terms: Public domain W3C validator