Mathbox for Jarvin Udandy < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  mdandyvrx4 Structured version   Unicode version

Theorem mdandyvrx4 32360
 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
mdandyvrx4.1
mdandyvrx4.2
mdandyvrx4.3
mdandyvrx4.4
mdandyvrx4.5
mdandyvrx4.6
Assertion
Ref Expression
mdandyvrx4

Proof of Theorem mdandyvrx4
StepHypRef Expression
1 mdandyvrx4.1 . . . . 5
2 mdandyvrx4.3 . . . . 5
31, 2axorbciffatcxorb 32303 . . . 4
4 mdandyvrx4.4 . . . . 5
51, 4axorbciffatcxorb 32303 . . . 4
63, 5pm3.2i 455 . . 3
7 mdandyvrx4.2 . . . 4
8 mdandyvrx4.5 . . . 4
97, 8axorbciffatcxorb 32303 . . 3
106, 9pm3.2i 455 . 2
11 mdandyvrx4.6 . . 3
121, 11axorbciffatcxorb 32303 . 2
1310, 12pm3.2i 455 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   wxo 1363 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 185  df-an 371  df-xor 1364 This theorem is referenced by:  mdandyvrx11  32367
 Copyright terms: Public domain W3C validator