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Theorem 3bior2fd 1468
Description: A wff is equivalent to its threefold disjunction with double falsehood, analogous to biorf 930. (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 930 . . 3 𝜒 → (𝜓 ↔ (𝜒𝜓)))
31, 2syl 17 . 2 (𝜑 → (𝜓 ↔ (𝜒𝜓)))
4 3biorfd.1 . . 3 (𝜑 → ¬ 𝜃)
543bior1fd 1466 . 2 (𝜑 → ((𝜒𝜓) ↔ (𝜃𝜒𝜓)))
63, 5bitrd 280 1 (𝜑 → (𝜓 ↔ (𝜃𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 207  wo 841  w3o 1078
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 208  df-or 842  df-3or 1080
This theorem is referenced by: (None)
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