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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  |-  ( (
ph  /\  ps )  <->  -.  ( -.  ph  \/  -.  ps ) )

Proof of Theorem anor
StepHypRef Expression
1 ianor 474 . . 3  |-  ( -.  ( ph  /\  ps ) 
<->  ( -.  ph  \/  -.  ps ) )
21bicomi 193 . 2  |-  ( ( -.  ph  \/  -.  ps )  <->  -.  ( ph  /\ 
ps ) )
32con2bii 322 1  |-  ( (
ph  /\  ps )  <->  -.  ( -.  ph  \/  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/ wo 357    /\ wa 358
This theorem is referenced by:  pm3.1  484  pm3.11  485  dn1  932  3anor  948  trlonprop  28341
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
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