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Theorem xorneg 1319
Description:  \/_ is unchanged under negation of both arguments. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
xorneg  |-  ( ( -.  ph  \/_  -.  ps ) 
<->  ( ph  \/_  ps ) )

Proof of Theorem xorneg
StepHypRef Expression
1 xorneg1 1317 . 2  |-  ( ( -.  ph  \/_  -.  ps ) 
<->  -.  ( ph  \/_  -.  ps ) )
2 xorneg2 1318 . . 3  |-  ( (
ph  \/_  -.  ps )  <->  -.  ( ph  \/_  ps ) )
32con2bii 323 . 2  |-  ( (
ph  \/_  ps )  <->  -.  ( ph  \/_  -.  ps ) )
41, 3bitr4i 244 1  |-  ( ( -.  ph  \/_  -.  ps ) 
<->  ( ph  \/_  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    \/_ wxo 1310
This theorem is referenced by:  hadnot  1399  had0  1409  mtp-xor  1542
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 178  df-xor 1311
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