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Theorem anor 509
 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 508 . . 3 (¬ (𝜑𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓))
21bicomi 213 . 2 ((¬ 𝜑 ∨ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
32con2bii 346 1 ((𝜑𝜓) ↔ ¬ (¬ 𝜑 ∨ ¬ 𝜓))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 195   ∨ wo 382   ∧ wa 383 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 196  df-or 384  df-an 385 This theorem is referenced by:  pm3.1  518  pm3.11  519  dn1  1000  3anor  1047  bropopvvv  7142  2wlkonot3v  26402  2spthonot3v  26403  ifpananb  36870  iunrelexp0  37013
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