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Theorem nbn 347
Description: The negation of a wff is equivalent to the wff's equivalence to falsehood. (Contributed by NM, 21-Jun-1993.) (Proof shortened by Wolf Lammen, 3-Oct-2013.)
Hypothesis
Ref Expression
nbn.1
Assertion
Ref Expression
nbn

Proof of Theorem nbn
StepHypRef Expression
1 nbn.1 . . 3
2 bibif 346 . . 3
31, 2ax-mp 5 . 2
43bicomi 202 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184
This theorem is referenced by:  nbn3  348  nbfal  1406  n0f  3793  disj  3867  axnulALT  4579  dm0rn0  5224  reldm0  5225  isarchi  27726
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
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