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Theorem anor 477
Description: Conjunction in terms of disjunction (DeMorgan'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  |-  ( (
ph  /\  ps )  <->  -.  ( -.  ph  \/  -.  ps ) )

Proof of Theorem anor
StepHypRef Expression
1 ianor 476 . . 3  |-  ( -.  ( ph  /\  ps ) 
<->  ( -.  ph  \/  -.  ps ) )
21bicomi 195 . 2  |-  ( ( -.  ph  \/  -.  ps )  <->  -.  ( ph  /\ 
ps ) )
32con2bii 324 1  |-  ( (
ph  /\  ps )  <->  -.  ( -.  ph  \/  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178    \/ wo 359    /\ wa 360
This theorem is referenced by:  pm3.1  486  pm3.11  487  dn1  937  3anor  953
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362
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