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Theorem ianor 474
 Description: Negated conjunction in terms of disjunction (De Morgan's law). Theorem *4.51 of [WhiteheadRussell] p. 120. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
ianor (¬ (φ ψ) ↔ (¬ φ ¬ ψ))

Proof of Theorem ianor
StepHypRef Expression
1 imnan 411 . 2 ((φ → ¬ ψ) ↔ ¬ (φ ψ))
2 pm4.62 408 . 2 ((φ → ¬ ψ) ↔ (¬ φ ¬ ψ))
31, 2bitr3i 242 1 (¬ (φ ψ) ↔ (¬ φ ¬ ψ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∨ wo 357   ∧ wa 358 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 This theorem is referenced by:  anor  475  3anor  948  cadnot  1394  19.33b  1608  neorian  2603  indifdir  3511  xpeq0  5046  imadif  5171  addceq0  6219
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