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Theorem anor 996
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 ianor 995 . . 3 (¬ (𝜑𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓))
21bicomi 215 . 2 ((¬ 𝜑 ∨ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
32con2bii 348 1 ((𝜑𝜓) ↔ ¬ (¬ 𝜑 ∨ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 197  wa 384  wo 865
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 198  df-an 385  df-or 866
This theorem is referenced by:  pm3.1  1005  pm3.11  1006  dn1  1073  3anorOLD  1123  bropopvvv  7499  ifpananb  38369  iunrelexp0  38512
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