MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nbn2 Unicode version

Theorem nbn2 345
Description: The negation of a wff is equivalent to the wff's equivalence to falsehood. (Contributed by Juha Arpiainen, 19-Jan-2006.) (Proof shortened by Wolf Lammen, 28-Jan-2013.)
Assertion
Ref Expression
nbn2

Proof of Theorem nbn2
StepHypRef Expression
1 pm5.501 341 . 2
2 notbi 295 . 2
31, 2syl6bbr 263 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184
This theorem is referenced by:  bibif  346  pm5.21im  349  pm5.18  356  biass  359  sadadd2lem2  14100  isclo  19588
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
  Copyright terms: Public domain W3C validator