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

Theorem orass 921
Description: Associative law for disjunction. Theorem *4.33 of [WhiteheadRussell] p. 118. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
orass (((𝜑𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))

Proof of Theorem orass
StepHypRef Expression
1 orcom 869 . 2 (((𝜑𝜓) ∨ 𝜒) ↔ (𝜒 ∨ (𝜑𝜓)))
2 or12 920 . 2 ((𝜒 ∨ (𝜑𝜓)) ↔ (𝜑 ∨ (𝜒𝜓)))
3 orcom 869 . . 3 ((𝜒𝜓) ↔ (𝜓𝜒))
43orbi2i 912 . 2 ((𝜑 ∨ (𝜒𝜓)) ↔ (𝜑 ∨ (𝜓𝜒)))
51, 2, 43bitri 297 1 (((𝜑𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wo 846
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 206  df-or 847
This theorem is referenced by:  pm2.31  922  pm2.32  923  or32  925  or4  926  3orass  1091  axi12  2706  axbnd  2707  unass  4131  tppreqb  4770  ltxr  13043  lcmass  16497  plydivex  25673  clwwlkneq0  29015  disjxpin  31548  wl-ifpimpr  35966  impor  36569  ifpim123g  41846
  Copyright terms: Public domain W3C validator