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Theorem nbn2 334
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  |-  ( -. 
ph  ->  ( -.  ps  <->  (
ph 
<->  ps ) ) )

Proof of Theorem nbn2
StepHypRef Expression
1 pm5.501 330 . 2  |-  ( -. 
ph  ->  ( -.  ps  <->  ( -.  ph  <->  -.  ps )
) )
2 notbi 286 . 2  |-  ( (
ph 
<->  ps )  <->  ( -.  ph  <->  -. 
ps ) )
31, 2syl6bbr 254 1  |-  ( -. 
ph  ->  ( -.  ps  <->  (
ph 
<->  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176
This theorem is referenced by:  bibif  335  pm5.21im  338  pm5.18  345  biass  348  sadadd2lem2  12641  isclo  16824
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177
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