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Theorem oranim 770
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  |-  ( (
ph  \/  ps )  ->  -.  ( -.  ph  /\ 
-.  ps ) )

Proof of Theorem oranim
StepHypRef Expression
1 pm4.56 769 . . 3  |-  ( ( -.  ph  /\  -.  ps ) 
<->  -.  ( ph  \/  ps ) )
21biimpi 119 . 2  |-  ( ( -.  ph  /\  -.  ps )  ->  -.  ( ph  \/  ps ) )
32con2i 616 1  |-  ( (
ph  \/  ps )  ->  -.  ( -.  ph  /\ 
-.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 103    \/ wo 697
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  unssin  3315  prneimg  3701  ftpg  5604  xrlttri3  9595
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