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Theorem anor 980
Description: Conjunction in terms of disjunction (De Morgan's law). Theorem *4.5 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 3-Nov-2012.)
Assertion
Ref Expression
anor ((𝜑𝜓) ↔ ¬ (¬ 𝜑 ∨ ¬ 𝜓))

Proof of Theorem anor
StepHypRef Expression
1 notnotb 315 . 2 ((𝜑𝜓) ↔ ¬ ¬ (𝜑𝜓))
2 ianor 979 . 2 (¬ (𝜑𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓))
31, 2xchbinx 334 1 ((𝜑𝜓) ↔ ¬ (¬ 𝜑 ∨ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205  wa 396  wo 844
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 206  df-an 397  df-or 845
This theorem is referenced by:  pm3.1  989  pm3.11  990  dn1  1055  noran  1531  bropopvvv  7922  swrdnd0  14381  ifpananb  41104  iunrelexp0  41292
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