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Theorem 3orcomb 1091
 Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011.) (Proof shortened by Wolf Lammen, 8-Apr-2022.)
Assertion
Ref Expression
3orcomb ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))

Proof of Theorem 3orcomb
StepHypRef Expression
1 3orcoma 1090 . 2 ((𝜑𝜓𝜒) ↔ (𝜓𝜑𝜒))
2 3orrot 1089 . 2 ((𝜓𝜑𝜒) ↔ (𝜑𝜒𝜓))
31, 2bitri 278 1 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209   ∨ w3o 1083 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  df-3or 1085 This theorem is referenced by:  eueq3  3627  swoso  8337  swrdnd  14068  colcom  26456  legso  26497  lncom  26520  soseq  33362  colinearperm1  33939  frege129d  40865  ordelordALT  41644  ordelordALTVD  41974
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