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Theorem dfnot 1307
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.) (Proof shortened by Wolf Lammen, 21-Jul-2019.)
Assertion
Ref Expression
dfnot  |-  ( -. 
ph 
<->  ( ph  -> F.  ) )

Proof of Theorem dfnot
StepHypRef Expression
1 fal 1296 . 2  |-  -. F.
2 mtt 645 . 2  |-  ( -. F.  ->  ( -.  ph  <->  (
ph  -> F.  ) ) )
31, 2ax-mp 7 1  |-  ( -. 
ph 
<->  ( ph  -> F.  ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 103   F. wfal 1294
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295
This theorem is referenced by:  inegd  1308  pclem6  1310  alnex  1433  alexim  1581  difin  3234  indifdir  3253  recvguniq  10393  bj-axempty2  11442
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