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 870 . 2 (((𝜑𝜓) ∨ 𝜒) ↔ (𝜒 ∨ (𝜑𝜓)))
2 or12 920 . 2 ((𝜒 ∨ (𝜑𝜓)) ↔ (𝜑 ∨ (𝜒𝜓)))
3 orcom 870 . . 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 206  wo 847
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 207  df-or 848
This theorem is referenced by:  pm2.31  922  pm2.32  923  or32  925  or4  926  3orass  1089  axi12  2704  axbnd  2705  unass  4182  tppreqb  4810  ltxr  13155  lcmass  16648  plydivex  26354  clwwlkneq0  30058  disjxpin  32608  wl-ifpimpr  37449  impor  38068  ifpim123g  43490
  Copyright terms: Public domain W3C validator