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Theorem excxor 1406
Description: This tautology shows that xor is really exclusive. (Contributed by FL, 22-Nov-2010.)
Assertion
Ref Expression
excxor  |-  ( (
ph  \/_  ps )  <->  ( ( ph  /\  -.  ps )  \/  ( -.  ph  /\  ps )
) )

Proof of Theorem excxor
StepHypRef Expression
1 df-xor 1401 . 2  |-  ( (
ph  \/_  ps )  <->  -.  ( ph  <->  ps )
)
2 xor 899 . 2  |-  ( -.  ( ph  <->  ps )  <->  ( ( ph  /\  -.  ps )  \/  ( ps  /\  -.  ph )
) )
3 ancom 451 . . 3  |-  ( ( ps  /\  -.  ph ) 
<->  ( -.  ph  /\  ps ) )
43orbi2i 521 . 2  |-  ( ( ( ph  /\  -.  ps )  \/  ( ps  /\  -.  ph )
)  <->  ( ( ph  /\ 
-.  ps )  \/  ( -.  ph  /\  ps )
) )
51, 2, 43bitri 274 1  |-  ( (
ph  \/_  ps )  <->  ( ( ph  /\  -.  ps )  \/  ( -.  ph  /\  ps )
) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    \/ wo 369    /\ wa 370    \/_ wxo 1400
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 188  df-or 371  df-an 372  df-xor 1401
This theorem is referenced by:  f1omvdco2  17032  psgnunilem5  17078
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