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Theorem xorcom 1366
Description:  \/_ is commutative. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
xorcom  |-  ( (
ph  \/_  ps )  <->  ( ps  \/_  ph ) )

Proof of Theorem xorcom
StepHypRef Expression
1 bicom 200 . . 3  |-  ( (
ph 
<->  ps )  <->  ( ps  <->  ph ) )
21notbii 296 . 2  |-  ( -.  ( ph  <->  ps )  <->  -.  ( ps  <->  ph ) )
3 df-xor 1364 . 2  |-  ( (
ph  \/_  ps )  <->  -.  ( ph  <->  ps )
)
4 df-xor 1364 . 2  |-  ( ( ps  \/_  ph )  <->  -.  ( ps 
<-> 
ph ) )
52, 3, 43bitr4i 277 1  |-  ( (
ph  \/_  ps )  <->  ( ps  \/_  ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/_ wxo 1363
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 1364
This theorem is referenced by:  xorneg2  1374  hadcoma  1455  hadcomb  1456  cadcoma  1462
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