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Theorem 3orcomb 1041
 Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011.)
Assertion
Ref Expression
3orcomb ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))

Proof of Theorem 3orcomb
StepHypRef Expression
1 orcom 401 . . 3 ((𝜓𝜒) ↔ (𝜒𝜓))
21orbi2i 540 . 2 ((𝜑 ∨ (𝜓𝜒)) ↔ (𝜑 ∨ (𝜒𝜓)))
3 3orass 1034 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
4 3orass 1034 . 2 ((𝜑𝜒𝜓) ↔ (𝜑 ∨ (𝜒𝜓)))
52, 3, 43bitr4i 291 1 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 195   ∨ wo 382   ∨ w3o 1030 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 196  df-or 384  df-3or 1032 This theorem is referenced by:  eueq3  3348  swoso  7662  swrdnd  13284  colcom  25253  legso  25294  lncom  25317  soseq  30995  colinearperm1  31339  frege129d  37074  ordelordALT  37768  ordelordALTVD  38125
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