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Theorem nbbn 360
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 359 . 2  |-  ( -.  ( ph  <->  ps )  <->  (
ph 
<->  -.  ps ) )
2 con2bi 330 . 2  |-  ( (
ph 
<->  -.  ps )  <->  ( ps  <->  -. 
ph ) )
3 bicom 204 . 2  |-  ( ( ps  <->  -.  ph )  <->  ( -.  ph  <->  ps ) )
41, 2, 33bitrri 276 1  |-  ( ( -.  ph  <->  ps )  <->  -.  ( ph 
<->  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 188
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 189
This theorem is referenced by:  biass  361  pclem6  941  xorass  1409  xorassOLD  1410  xorneg1OLD  1418  trubifalOLD  1483  hadbi  1501  canth  6249  qextltlem  11495  onint1  31109  notbinot1  32312  notbinot2  32316
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