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Theorem 3orcoma 1078
Description: Commutation law for triple disjunction. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
3orcoma ((𝜑𝜓𝜒) ↔ (𝜓𝜑𝜒))

Proof of Theorem 3orcoma
StepHypRef Expression
1 or12 546 . 2 ((𝜑 ∨ (𝜓𝜒)) ↔ (𝜓 ∨ (𝜑𝜒)))
2 3orass 1075 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
3 3orass 1075 . 2 ((𝜓𝜑𝜒) ↔ (𝜓 ∨ (𝜑𝜒)))
41, 2, 33bitr4i 292 1 ((𝜑𝜓𝜒) ↔ (𝜓𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wo 382  w3o 1071
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 384  df-3or 1073
This theorem is referenced by:  3orcomb  1079  outpasch  25846  eliccioo  29948
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