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Theorem nbbn 358
Description: Move negation outside of biconditional. Compare Theorem *5.18 of [WhiteheadRussell] p. 124. (Contributed by NM, 27-Jun-2002.) (Proof shortened by Wolf Lammen, 20-Sep-2013.)
Assertion
Ref Expression
nbbn  |-  ( ( -.  ph  <->  ps )  <->  -.  ( ph 
<->  ps ) )

Proof of Theorem nbbn
StepHypRef Expression
1 xor3 357 . 2  |-  ( -.  ( ph  <->  ps )  <->  (
ph 
<->  -.  ps ) )
2 con2bi 328 . 2  |-  ( (
ph 
<->  -.  ps )  <->  ( ps  <->  -. 
ph ) )
3 bicom 200 . 2  |-  ( ( ps  <->  -.  ph )  <->  ( -.  ph  <->  ps ) )
41, 2, 33bitrri 272 1  |-  ( ( -.  ph  <->  ps )  <->  -.  ( ph 
<->  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184
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
This theorem is referenced by:  biass  359  pclem6  921  xorass  1355  xorneg1  1361  trubifal  1409  hadbi  1429  canth  6161  qextltlem  11287  onint1  28462  notbinot1  29050  notbinot2  29054
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