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Theorem 3bior1fand 1437
Description: A disjunction is equivalent to a threefold disjunction with single falsehood of a conjunction. (Contributed by Alexander van der Vekens, 8-Sep-2017.)
Hypothesis
Ref Expression
3biorfd.1 (𝜑 → ¬ 𝜃)
Assertion
Ref Expression
3bior1fand (𝜑 → ((𝜒𝜓) ↔ ((𝜃𝜏) ∨ 𝜒𝜓)))

Proof of Theorem 3bior1fand
StepHypRef Expression
1 3biorfd.1 . . 3 (𝜑 → ¬ 𝜃)
21intnanrd 962 . 2 (𝜑 → ¬ (𝜃𝜏))
323bior1fd 1436 1 (𝜑 → ((𝜒𝜓) ↔ ((𝜃𝜏) ∨ 𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wo 383  wa 384  w3o 1035
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
This theorem is referenced by: (None)
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