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Theorem xorneg2 1426
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
xorneg2  |-  ( (
ph  \/_  -.  ps )  <->  -.  ( ph  \/_  ps ) )

Proof of Theorem xorneg2
StepHypRef Expression
1 df-xor 1416 . 2  |-  ( (
ph  \/_  -.  ps )  <->  -.  ( ph  <->  -.  ps )
)
2 pm5.18 362 . 2  |-  ( (
ph 
<->  ps )  <->  -.  ( ph 
<->  -.  ps ) )
3 xnor 1417 . 2  |-  ( (
ph 
<->  ps )  <->  -.  ( ph  \/_  ps ) )
41, 2, 33bitr2i 281 1  |-  ( (
ph  \/_  -.  ps )  <->  -.  ( ph  \/_  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 189    \/_ wxo 1415
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 190  df-xor 1416
This theorem is referenced by:  xorneg1  1427  xorneg  1430
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