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Theorem 3orcomb 933
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 682 . . 3 ((𝜓𝜒) ↔ (𝜒𝜓))
21orbi2i 714 . 2 ((𝜑 ∨ (𝜓𝜒)) ↔ (𝜑 ∨ (𝜒𝜓)))
3 3orass 927 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
4 3orass 927 . 2 ((𝜑𝜒𝜓) ↔ (𝜑 ∨ (𝜒𝜓)))
52, 3, 43bitr4i 210 1 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
Colors of variables: wff set class
Syntax hints:  wb 103  wo 664  w3o 923
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665
This theorem depends on definitions:  df-bi 115  df-3or 925
This theorem is referenced by:  eueq3dc  2787  sotritrieq  4143
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