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Theorem ioran 476
 Description: Negated disjunction in terms of conjunction (De Morgan's law). Compare Theorem *4.56 of [WhiteheadRussell] p. 120. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Assertion
Ref Expression
ioran (¬ (φ ψ) ↔ (¬ φ ¬ ψ))

Proof of Theorem ioran
StepHypRef Expression
1 pm4.65 416 . 2 (¬ (¬ φψ) ↔ (¬ φ ¬ ψ))
2 pm4.64 361 . 2 ((¬ φψ) ↔ (φ ψ))
31, 2xchnxbi 299 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:  pm4.56  481  oibabs  851  xor  861  3ioran  950  3ori  1242  ecase23d  1285  19.43OLD  1606  equvini  1987  2ralor  2780  dfun2  3490  sfin111  4536  nchoice  6308
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