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Theorem orass 919
 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 867 . 2 (((𝜑𝜓) ∨ 𝜒) ↔ (𝜒 ∨ (𝜑𝜓)))
2 or12 918 . 2 ((𝜒 ∨ (𝜑𝜓)) ↔ (𝜑 ∨ (𝜒𝜓)))
3 orcom 867 . . 3 ((𝜒𝜓) ↔ (𝜓𝜒))
43orbi2i 910 . 2 ((𝜑 ∨ (𝜒𝜓)) ↔ (𝜑 ∨ (𝜓𝜒)))
51, 2, 43bitri 300 1 (((𝜑𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209   ∨ wo 844 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 210  df-or 845 This theorem is referenced by:  pm2.31  920  pm2.32  921  or32  923  or4  924  3orass  1087  axi12  2768  axbnd  2769  unass  4093  tppreqb  4698  ltxr  12501  lcmass  15951  plydivex  24903  clwwlkneq0  27824  disjxpin  30361  wl-ifpimpr  34902  impor  35538  ifpim123g  40251
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