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Theorem xorneg1 1361
Description:  \/_ is negated under negation of one argument. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
xorneg1  |-  ( ( -.  ph  \/_  ps )  <->  -.  ( ph  \/_  ps ) )

Proof of Theorem xorneg1
StepHypRef Expression
1 df-xor 1352 . 2  |-  ( ( -.  ph  \/_  ps )  <->  -.  ( -.  ph  <->  ps )
)
2 nbbn 358 . . 3  |-  ( ( -.  ph  <->  ps )  <->  -.  ( ph 
<->  ps ) )
32con2bii 332 . 2  |-  ( (
ph 
<->  ps )  <->  -.  ( -.  ph  <->  ps ) )
4 xnor 1353 . 2  |-  ( (
ph 
<->  ps )  <->  -.  ( ph  \/_  ps ) )
51, 3, 43bitr2i 273 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:  xorneg2  1362  xorneg  1363
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