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Theorem 3oran 1055
Description: Triple disjunction in terms of triple conjunction. (Contributed by NM, 8-Oct-2012.)
Assertion
Ref Expression
3oran ((𝜑𝜓𝜒) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓 ∧ ¬ 𝜒))

Proof of Theorem 3oran
StepHypRef Expression
1 3ioran 1054 . . 3 (¬ (𝜑𝜓𝜒) ↔ (¬ 𝜑 ∧ ¬ 𝜓 ∧ ¬ 𝜒))
21con1bii 346 . 2 (¬ (¬ 𝜑 ∧ ¬ 𝜓 ∧ ¬ 𝜒) ↔ (𝜑𝜓𝜒))
32bicomi 214 1 ((𝜑𝜓𝜒) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓 ∧ ¬ 𝜒))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  w3o 1035  w3a 1036
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-an 386  df-3or 1037  df-3an 1038
This theorem is referenced by:  nolt02o  31819  nosupbnd1lem6  31833  dalawlem10  34985
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