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Theorem excxor 1268
Description: This tautology shows that xor is really exclusive. (Contributed by FL, 22-Nov-2010.) (Proof rewritten by Jim Kingdon, 5-May-2018.)
Assertion
Ref Expression
excxor  \/_

Proof of Theorem excxor
StepHypRef Expression
1 xoranor 1267 . . 3  \/_
2 andi 730 . . 3
3 orcom 646 . . . . 5
4 pm3.24 626 . . . . . 6
54biorfi 664 . . . . 5
6 andir 731 . . . . 5
73, 5, 63bitr4ri 202 . . . 4
8 pm5.61 707 . . . 4
97, 8orbi12i 680 . . 3
101, 2, 93bitri 195 . 2  \/_
11 orcom 646 . 2
12 ancom 253 . . 3
1312orbi2i 678 . 2
1410, 11, 133bitri 195 1  \/_
Colors of variables: wff set class
Syntax hints:   wn 3   wa 97   wb 98   wo 628    \/_ wxo 1265
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-xor 1266
This theorem is referenced by:  xordc  1280  symdifxor  3197
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