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Theorem nbn 336
Description: The negation of a wff is equivalent to the wff's equivalence to falsehood. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Oct-2013.)
Hypothesis
Ref Expression
nbn.1  |-  -.  ph
Assertion
Ref Expression
nbn  |-  ( -. 
ps 
<->  ( ps  <->  ph ) )

Proof of Theorem nbn
StepHypRef Expression
1 nbn.1 . . 3  |-  -.  ph
2 bibif 335 . . 3  |-  ( -. 
ph  ->  ( ( ps  <->  ph )  <->  -.  ps )
)
31, 2ax-mp 8 . 2  |-  ( ( ps  <->  ph )  <->  -.  ps )
43bicomi 193 1  |-  ( -. 
ps 
<->  ( ps  <->  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176
This theorem is referenced by:  nbn3  337  nbfal  1316  n0f  3463  disj  3495  axnulALT  4147  dm0rn0  4895  reldm0  4896
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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