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Theorem nannot 1293
Description: Show equivalence between negation and the Nicod version. To derive nic-dfneg 1425, apply nanbi 1294. (Contributed by Jeff Hoffman, 19-Nov-2007.)
Assertion
Ref Expression
nannot  |-  ( -. 
ps 
<->  ( ps  -/\  ps )
)

Proof of Theorem nannot
StepHypRef Expression
1 df-nan 1288 . . 3  |-  ( ( ps  -/\  ps )  <->  -.  ( ps  /\  ps ) )
2 anidm 625 . . 3  |-  ( ( ps  /\  ps )  <->  ps )
31, 2xchbinx 301 . 2  |-  ( ( ps  -/\  ps )  <->  -. 
ps )
43bicomi 193 1  |-  ( -. 
ps 
<->  ( ps  -/\  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    /\ wa 358    -/\ wnan 1287
This theorem is referenced by:  nanbi  1294  trunantru  1344  falnanfal  1347  nic-dfneg  1425  andnand1  24837  imnand2  24838
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-an 360  df-nan 1288
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