MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  xorneg Unicode version

Theorem xorneg 1322
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 1320 . 2  |-  ( ( -.  ph  \/_  -.  ps ) 
<->  -.  ( ph  \/_  -.  ps ) )
2 xorneg2 1321 . . 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 1313
This theorem is referenced by:  hadnot  1402  had0  1412  mtp-xor  1545
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 1314
  Copyright terms: Public domain W3C validator