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Theorem xorneg 1363
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 1361 . 2  |-  ( ( -.  ph  \/_  -.  ps ) 
<->  -.  ( ph  \/_  -.  ps ) )
2 xorneg2 1362 . . 3  |-  ( (
ph  \/_  -.  ps )  <->  -.  ( ph  \/_  ps ) )
32con2bii 332 . 2  |-  ( (
ph  \/_  ps )  <->  -.  ( ph  \/_  -.  ps ) )
41, 3bitr4i 252 1  |-  ( ( -.  ph  \/_  -.  ps ) 
<->  ( ph  \/_  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/_ wxo 1351
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  df-xor 1352
This theorem is referenced by:  hadnot  1436  had0  1446
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