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Theorem nannot 1339
Description: Show equivalence between negation and the Nicod version. To derive nic-dfneg 1477, apply nanbi 1340. (Contributed by Jeff Hoffman, 19-Nov-2007.)
Assertion
Ref Expression
nannot  |-  ( -. 
ps 
<->  ( ps  -/\  ps )
)

Proof of Theorem nannot
StepHypRef Expression
1 df-nan 1334 . . 3  |-  ( ( ps  -/\  ps )  <->  -.  ( ps  /\  ps ) )
2 anidm 644 . . 3  |-  ( ( ps  /\  ps )  <->  ps )
31, 2xchbinx 310 . 2  |-  ( ( ps  -/\  ps )  <->  -. 
ps )
43bicomi 202 1  |-  ( -. 
ps 
<->  ( ps  -/\  ps )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    /\ wa 369    -/\ wnan 1333
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 185  df-an 371  df-nan 1334
This theorem is referenced by:  nanbi  1340  trunantru  1411  falnanfal  1414  nic-dfneg  1477  andnand1  28245  imnand2  28246
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