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Theorem 3orcomb 1046
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 402 . . 3 ((𝜓𝜒) ↔ (𝜒𝜓))
21orbi2i 541 . 2 ((𝜑 ∨ (𝜓𝜒)) ↔ (𝜑 ∨ (𝜒𝜓)))
3 3orass 1039 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
4 3orass 1039 . 2 ((𝜑𝜒𝜓) ↔ (𝜑 ∨ (𝜒𝜓)))
52, 3, 43bitr4i 292 1 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wo 383  w3o 1035
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 197  df-or 385  df-3or 1037
This theorem is referenced by:  eueq3  3368  swoso  7721  swrdnd  13365  colcom  25348  legso  25389  lncom  25412  soseq  31444  colinearperm1  31803  frege129d  37522  ordelordALT  38215  ordelordALTVD  38572
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