MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  excxor Unicode version

Theorem excxor 1300
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 1296 . 2  |-  ( (
ph \/_ ps )  <->  -.  ( ph 
<->  ps ) )
2 xor 861 . 2  |-  ( -.  ( ph  <->  ps )  <->  ( ( ph  /\  -.  ps )  \/  ( ps  /\  -.  ph )
) )
3 ancom 437 . . 3  |-  ( ( ps  /\  -.  ph ) 
<->  ( -.  ph  /\  ps ) )
43orbi2i 505 . 2  |-  ( ( ( ph  /\  -.  ps )  \/  ( ps  /\  -.  ph )
)  <->  ( ( ph  /\ 
-.  ps )  \/  ( -.  ph  /\  ps )
) )
51, 2, 43bitri 262 1  |-  ( (
ph \/_ ps )  <->  ( ( ph  /\  -.  ps )  \/  ( -.  ph  /\  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/ wo 357    /\ wa 358   \/_wxo 1295
This theorem is referenced by:  f1omvdco2  27391  psgnunilem5  27417
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  df-xor 1296
  Copyright terms: Public domain W3C validator