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Theorem 3ioran 950
 Description: Negated triple disjunction as triple conjunction. (Contributed by Scott Fenton, 19-Apr-2011.)
Assertion
Ref Expression
3ioran (¬ (φ ψ χ) ↔ (¬ φ ¬ ψ ¬ χ))

Proof of Theorem 3ioran
StepHypRef Expression
1 ioran 476 . . 3 (¬ (φ ψ) ↔ (¬ φ ¬ ψ))
21anbi1i 676 . 2 ((¬ (φ ψ) ¬ χ) ↔ ((¬ φ ¬ ψ) ¬ χ))
3 ioran 476 . . 3 (¬ ((φ ψ) χ) ↔ (¬ (φ ψ) ¬ χ))
4 df-3or 935 . . 3 ((φ ψ χ) ↔ ((φ ψ) χ))
53, 4xchnxbir 300 . 2 (¬ (φ ψ χ) ↔ (¬ (φ ψ) ¬ χ))
6 df-3an 936 . 2 ((¬ φ ¬ ψ ¬ χ) ↔ ((¬ φ ¬ ψ) ¬ χ))
72, 5, 63bitr4i 268 1 (¬ (φ ψ χ) ↔ (¬ φ ¬ ψ ¬ χ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 176   ∨ wo 357   ∧ wa 358   ∨ w3o 933   ∧ w3a 934 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936 This theorem is referenced by:  3oran  951  cadnot  1394
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