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Theorem oranim 800
Description: Disjunction in terms of conjunction (DeMorgan's law). One direction of Theorem *4.57 of [WhiteheadRussell] p. 120. The converse does not hold intuitionistically but does hold in classical logic. (Contributed by Jim Kingdon, 25-Jul-2018.)
Assertion
Ref Expression
oranim ((φ ψ) → ¬ (¬ φ ¬ ψ))

Proof of Theorem oranim
StepHypRef Expression
1 pm4.56 799 . . 3 ((¬ φ ¬ ψ) ↔ ¬ (φ ψ))
21biimpi 113 . 2 ((¬ φ ¬ ψ) → ¬ (φ ψ))
32con2i 545 1 ((φ ψ) → ¬ (¬ φ ¬ ψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97   wo 616
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-io 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  unssin  3154  prneimg  3497  ftpg  5239
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