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Theorem 3bior2fd 1474
 Description: A wff is equivalent to its threefold disjunction with double falsehood, analogous to biorf 934. (Contributed by Alexander van der Vekens, 8-Sep-2017.)
Hypotheses
Ref Expression
3biorfd.1 (𝜑 → ¬ 𝜃)
3biorfd.2 (𝜑 → ¬ 𝜒)
Assertion
Ref Expression
3bior2fd (𝜑 → (𝜓 ↔ (𝜃𝜒𝜓)))

Proof of Theorem 3bior2fd
StepHypRef Expression
1 3biorfd.2 . . 3 (𝜑 → ¬ 𝜒)
2 biorf 934 . . 3 𝜒 → (𝜓 ↔ (𝜒𝜓)))
31, 2syl 17 . 2 (𝜑 → (𝜓 ↔ (𝜒𝜓)))
4 3biorfd.1 . . 3 (𝜑 → ¬ 𝜃)
543bior1fd 1472 . 2 (𝜑 → ((𝜒𝜓) ↔ (𝜃𝜒𝜓)))
63, 5bitrd 282 1 (𝜑 → (𝜓 ↔ (𝜃𝜒𝜓)))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 209   ∨ wo 844   ∨ w3o 1083 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 210  df-or 845  df-3or 1085 This theorem is referenced by: (None)
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