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Theorem anor 491
Description: Conjunction in terms of disjunction (De Morgan's law). Theorem *4.5 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-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 490 . . 3  |-  ( -.  ( ph  /\  ps ) 
<->  ( -.  ph  \/  -.  ps ) )
21bicomi 205 . 2  |-  ( ( -.  ph  \/  -.  ps )  <->  -.  ( ph  /\ 
ps ) )
32con2bii 333 1  |-  ( (
ph  /\  ps )  <->  -.  ( -.  ph  \/  -.  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    \/ wo 369    /\ wa 370
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 188  df-or 371  df-an 372
This theorem is referenced by:  pm3.1  500  pm3.11  501  dn1  974  3anor  998  bropopvvv  6887  2wlkonot3v  25448  2spthonot3v  25449  ifpananb  35848  iunrelexp0  35932
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