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Theorem mdandyvrx12 28041
 Description: Given the exclusivities set in the hypotheses, there exist a proof where ch, th, ta, et exclude ze, si accordingly (Contributed by Jarvin Udandy, 7-Sep-2016.)
Hypotheses
Ref Expression
mdandyvrx12.1
mdandyvrx12.2
mdandyvrx12.3
mdandyvrx12.4
mdandyvrx12.5
mdandyvrx12.6
Assertion
Ref Expression
mdandyvrx12

Proof of Theorem mdandyvrx12
StepHypRef Expression
1 mdandyvrx12.1 . . . . 5
2 mdandyvrx12.3 . . . . 5
31, 2axorbciffatcxorb 27976 . . . 4
4 mdandyvrx12.4 . . . . 5
51, 4axorbciffatcxorb 27976 . . . 4
63, 5pm3.2i 441 . . 3
7 mdandyvrx12.2 . . . 4
8 mdandyvrx12.5 . . . 4
97, 8axorbciffatcxorb 27976 . . 3
106, 9pm3.2i 441 . 2
11 mdandyvrx12.6 . . 3
127, 11axorbciffatcxorb 27976 . 2
1310, 12pm3.2i 441 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358   wxo 1295 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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