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Theorem anor 475
Description: Conjunction in terms of disjunction (De Morgan's law). Theorem *4.5 of [WhiteheadRussell] p. 120. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Nov-2012.)
Assertion
Ref Expression
anor ((φ ψ) ↔ ¬ (¬ φ ¬ ψ))

Proof of Theorem anor
StepHypRef Expression
1 ianor 474 . . 3 (¬ (φ ψ) ↔ (¬ φ ¬ ψ))
21bicomi 193 . 2 ((¬ φ ¬ ψ) ↔ ¬ (φ ψ))
32con2bii 322 1 ((φ ψ) ↔ ¬ (¬ φ ¬ ψ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176   wo 357   wa 358
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 177  df-or 359  df-an 360
This theorem is referenced by:  pm3.1  484  pm3.11  485  dn1  932  3anor  948  ltcirr  6272
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