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Theorem nannot 1303
Description: Show equivalence between negation and the Nicod version. To derive nic-dfneg 1445, apply nanbi 1304. (Contributed by Jeff Hoffman, 19-Nov-2007.)
Assertion
Ref Expression
nannot  |-  ( -. 
ps 
<->  ( ps  -/\  ps )
)

Proof of Theorem nannot
StepHypRef Expression
1 df-nan 1298 . . 3  |-  ( ( ps  -/\  ps )  <->  -.  ( ps  /\  ps ) )
2 anidm 627 . . 3  |-  ( ( ps  /\  ps )  <->  ps )
31, 2xchbinx 303 . 2  |-  ( ( ps  -/\  ps )  <->  -. 
ps )
43bicomi 195 1  |-  ( -. 
ps 
<->  ( ps  -/\  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 178    /\ wa 360    -/\ wnan 1297
This theorem is referenced by:  nanbi  1304  trunantru  1364  falnanfal  1367  nic-dfneg  1445  andnand1  26153  imnand2  26154
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 179  df-an 362  df-nan 1298
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