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Theorem xor2 1366
Description: Two ways to express "exclusive or." (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
xor2  |-  ( (
ph  \/_  ps )  <->  ( ( ph  \/  ps )  /\  -.  ( ph  /\ 
ps ) ) )

Proof of Theorem xor2
StepHypRef Expression
1 df-xor 1361 . 2  |-  ( (
ph  \/_  ps )  <->  -.  ( ph  <->  ps )
)
2 nbi2 890 . 2  |-  ( -.  ( ph  <->  ps )  <->  ( ( ph  \/  ps )  /\  -.  ( ph  /\ 
ps ) ) )
31, 2bitri 249 1  |-  ( (
ph  \/_  ps )  <->  ( ( ph  \/  ps )  /\  -.  ( ph  /\ 
ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/ wo 368    /\ wa 369    \/_ wxo 1360
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-or 370  df-an 371  df-xor 1361
This theorem is referenced by:  xoror  1367  xornan  1368  cador  1442  cad1  1450  saddisjlem  13973
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