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Theorem xorneg1 1374
Description:  \/_ is negated under negation of one argument. (Contributed by Mario Carneiro, 4-Sep-2016.) (Proof shortened by Wolf Lammen, 27-Jun-2020.)
Assertion
Ref Expression
xorneg1  |-  ( ( -.  ph  \/_  ps )  <->  -.  ( ph  \/_  ps ) )

Proof of Theorem xorneg1
StepHypRef Expression
1 xorcom 1365 . 2  |-  ( ( -.  ph  \/_  ps )  <->  ( ps  \/_  -.  ph )
)
2 xorneg2 1373 . . 3  |-  ( ( ps  \/_  -.  ph )  <->  -.  ( ps  \/_  ph )
)
3 xorcom 1365 . . 3  |-  ( ( ps  \/_  ph )  <->  ( ph  \/_ 
ps ) )
42, 3xchbinx 308 . 2  |-  ( ( ps  \/_  -.  ph )  <->  -.  ( ph  \/_  ps ) )
51, 4bitri 249 1  |-  ( ( -.  ph  \/_  ps )  <->  -.  ( ph  \/_  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/_ wxo 1362
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 1363
This theorem is referenced by:  xorneg2OLD  1376  xorneg  1377
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