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Theorem xor3 363
Description: Two ways to express "exclusive or." (Contributed by NM, 1-Jan-2006.)
Assertion
Ref Expression
xor3  |-  ( -.  ( ph  <->  ps )  <->  (
ph 
<->  -.  ps ) )

Proof of Theorem xor3
StepHypRef Expression
1 pm5.18 362 . . 3  |-  ( (
ph 
<->  ps )  <->  -.  ( ph 
<->  -.  ps ) )
21con2bii 338 . 2  |-  ( (
ph 
<->  -.  ps )  <->  -.  ( ph 
<->  ps ) )
32bicomi 207 1  |-  ( -.  ( ph  <->  ps )  <->  (
ph 
<->  -.  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 189
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
This theorem is referenced by:  nbbn  364  pm5.15  905  nbi2  908  xorass  1419  hadnot  1516  nabbi  2737  symdifass  3684  notzfaus  4595  nmogtmnf  26467  nmopgtmnf  27577  limsucncmpi  31155  aiffnbandciffatnotciffb  38626  axorbciffatcxorb  38627  abnotbtaxb  38638
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