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Theorem mdandyvrx3 27905
 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
mdandyvrx3.1
mdandyvrx3.2
mdandyvrx3.3
mdandyvrx3.4
mdandyvrx3.5
mdandyvrx3.6
Assertion
Ref Expression
mdandyvrx3

Proof of Theorem mdandyvrx3
StepHypRef Expression
1 mdandyvrx3.2 . . . . 5
2 mdandyvrx3.3 . . . . 5
31, 2axorbciffatcxorb 27849 . . . 4
4 mdandyvrx3.4 . . . . 5
51, 4axorbciffatcxorb 27849 . . . 4
63, 5pm3.2i 442 . . 3
7 mdandyvrx3.1 . . . 4
8 mdandyvrx3.5 . . . 4
97, 8axorbciffatcxorb 27849 . . 3
106, 9pm3.2i 442 . 2
11 mdandyvrx3.6 . . 3
127, 11axorbciffatcxorb 27849 . 2
1310, 12pm3.2i 442 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wxo 1313 This theorem is referenced by:  mdandyvrx12  27914 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 178  df-an 361  df-xor 1314
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