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Theorem dfnot 1342
Description: Given falsum, we can define the negation of a wff 
ph as the statement that a contradiction follows from assuming  ph. (Contributed by Mario Carneiro, 9-Feb-2017.)
Assertion
Ref Expression
dfnot  |-  ( -. 
ph 
<->  ( ph  ->  F.  ) )

Proof of Theorem dfnot
StepHypRef Expression
1 pm2.21 103 . 2  |-  ( -. 
ph  ->  ( ph  ->  F.  ) )
2 id 21 . . 3  |-  ( -. 
ph  ->  -.  ph )
3 falim 1338 . . 3  |-  (  F. 
->  -.  ph )
42, 3ja 156 . 2  |-  ( (
ph  ->  F.  )  ->  -. 
ph )
51, 4impbii 182 1  |-  ( -. 
ph 
<->  ( ph  ->  F.  ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 178    F. wfal 1327
This theorem is referenced by:  inegd  1343
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-tru 1329  df-fal 1330
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