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Theorem abnotbtaxb 27987
 Description: Assuming a, not b, there exists a proof a-xor-b.) (Contributed by Jarvin Udandy, 31-Aug-2016.)
Hypotheses
Ref Expression
abnotbtaxb.1
abnotbtaxb.2
Assertion
Ref Expression
abnotbtaxb

Proof of Theorem abnotbtaxb
StepHypRef Expression
1 abnotbtaxb.1 . . . 4
2 abnotbtaxb.2 . . . 4
31, 2pm3.2i 441 . . 3
4 xor3 346 . . . . . . 7
5 pm5.1 830 . . . . . . . . 9
6 ibibr 332 . . . . . . . . . 10
76biimpi 186 . . . . . . . . 9
85, 7ax-mp 8 . . . . . . . 8
93, 8ax-mp 8 . . . . . . 7
104, 9pm3.2i 441 . . . . . 6
11 bitr 689 . . . . . 6
1210, 11ax-mp 8 . . . . 5
13 bicom 191 . . . . . 6
1413biimpi 186 . . . . 5
1512, 14ax-mp 8 . . . 4
1615biimpi 186 . . 3
173, 16ax-mp 8 . 2
18 df-xor 1296 . . . 4
19 bicom 191 . . . . 5
2019biimpi 186 . . . 4
2118, 20ax-mp 8 . . 3
2221biimpi 186 . 2
2317, 22ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358   wxo 1295 This theorem is referenced by:  aistbisfiaxb  27991 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-an 360  df-xor 1296
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