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Theorem abnotataxb 27885
 Description: Assuming not a, b, there exists a proof a-xor-b.) (Contributed by Jarvin Udandy, 31-Aug-2016.)
Hypotheses
Ref Expression
abnotataxb.1
abnotataxb.2
Assertion
Ref Expression
abnotataxb

Proof of Theorem abnotataxb
StepHypRef Expression
1 abnotataxb.1 . . . . . . 7
2 abnotataxb.2 . . . . . . 7
31, 2pm3.2i 441 . . . . . 6
4 pm3.22 436 . . . . . 6
53, 4ax-mp 8 . . . . 5
6 orc 374 . . . . 5
75, 6ax-mp 8 . . . 4
8 pm1.4 375 . . . 4
97, 8ax-mp 8 . . 3
10 xor 861 . . . . 5
11 bicom 191 . . . . . 6
1211biimpi 186 . . . . 5
1310, 12ax-mp 8 . . . 4
1413biimpi 186 . . 3
159, 14ax-mp 8 . 2
16 df-xor 1296 . . . 4
17 bicom 191 . . . . 5
1817biimpi 186 . . . 4
1916, 18ax-mp 8 . . 3
2019biimpi 186 . 2
2115, 20ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 176   wo 357   wa 358  wxo 1295 This theorem is referenced by:  aisfbistiaxb  27889 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
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