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Theorem nbi2 862
Description: Two ways to express "exclusive or." (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Jan-2013.)
Assertion
Ref Expression
nbi2  |-  ( -.  ( ph  <->  ps )  <->  ( ( ph  \/  ps )  /\  -.  ( ph  /\ 
ps ) ) )

Proof of Theorem nbi2
StepHypRef Expression
1 xor3 346 . 2  |-  ( -.  ( ph  <->  ps )  <->  (
ph 
<->  -.  ps ) )
2 pm5.17 858 . 2  |-  ( ( ( ph  \/  ps )  /\  -.  ( ph  /\ 
ps ) )  <->  ( ph  <->  -. 
ps ) )
31, 2bitr4i 243 1  |-  ( -.  ( ph  <->  ps )  <->  ( ( ph  \/  ps )  /\  -.  ( ph  /\ 
ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/ wo 357    /\ wa 358
This theorem is referenced by:  xor2  1301  nmogtmnf  21348  nmopgtmnf  22448
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
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