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Theorem 3ianor 949
Description: Negated triple conjunction expressed in terms of triple disjunction. (Contributed by Jeff Hankins, 15-Aug-2009.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
3ianor (¬ (φ ψ χ) ↔ (¬ φ ¬ ψ ¬ χ))

Proof of Theorem 3ianor
StepHypRef Expression
1 3anor 948 . . 3 ((φ ψ χ) ↔ ¬ (¬ φ ¬ ψ ¬ χ))
21con2bii 322 . 2 ((¬ φ ¬ ψ ¬ χ) ↔ ¬ (φ ψ χ))
32bicomi 193 1 (¬ (φ ψ χ) ↔ (¬ φ ¬ ψ ¬ χ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176   w3o 933   w3a 934
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 177  df-or 359  df-an 360  df-3or 935  df-3an 936
This theorem is referenced by: (None)
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