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Theorem xorneg2 1373
Description:  \/_ is negated under negation of one argument. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
xorneg2  |-  ( (
ph  \/_  -.  ps )  <->  -.  ( ph  \/_  ps ) )

Proof of Theorem xorneg2
StepHypRef Expression
1 xorneg1 1372 . 2  |-  ( ( -.  ps  \/_  ph )  <->  -.  ( ps  \/_  ph )
)
2 xorcom 1365 . 2  |-  ( (
ph  \/_  -.  ps )  <->  ( -.  ps  \/_  ph )
)
3 xorcom 1365 . . 3  |-  ( (
ph  \/_  ps )  <->  ( ps  \/_  ph ) )
43notbii 296 . 2  |-  ( -.  ( ph  \/_  ps ) 
<->  -.  ( ps  \/_  ph ) )
51, 2, 43bitr4i 277 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:  xorneg  1374  hadnot  1446
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