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Theorem 3orcomb 987
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 728 . . 3 ((𝜓𝜒) ↔ (𝜒𝜓))
21orbi2i 762 . 2 ((𝜑 ∨ (𝜓𝜒)) ↔ (𝜑 ∨ (𝜒𝜓)))
3 3orass 981 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
4 3orass 981 . 2 ((𝜑𝜒𝜓) ↔ (𝜑 ∨ (𝜒𝜓)))
52, 3, 43bitr4i 212 1 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
Colors of variables: wff set class
Syntax hints:  wb 105  wo 708  w3o 977
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709
This theorem depends on definitions:  df-bi 117  df-3or 979
This theorem is referenced by:  eueq3dc  2912  sotritrieq  4326  exmidontriimlem3  7222
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