Users' Mathboxes Mathbox for Jarvin Udandy < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  mdandyvrx14 Unicode version

Theorem mdandyvrx14 27940
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
mdandyvrx14.1  |-  ( ph \/_ ze )
mdandyvrx14.2  |-  ( ps
\/_ si )
mdandyvrx14.3  |-  ( ch  <->  ph )
mdandyvrx14.4  |-  ( th  <->  ps )
mdandyvrx14.5  |-  ( ta  <->  ps )
mdandyvrx14.6  |-  ( et  <->  ps )
Assertion
Ref Expression
mdandyvrx14  |-  ( ( ( ( ch \/_ ze )  /\  ( th \/_ si ) )  /\  ( ta \/_ si ) )  /\  ( et \/_ si ) )

Proof of Theorem mdandyvrx14
StepHypRef Expression
1 mdandyvrx14.1 . . . . 5  |-  ( ph \/_ ze )
2 mdandyvrx14.3 . . . . 5  |-  ( ch  <->  ph )
31, 2axorbciffatcxorb 27873 . . . 4  |-  ( ch
\/_ ze )
4 mdandyvrx14.2 . . . . 5  |-  ( ps
\/_ si )
5 mdandyvrx14.4 . . . . 5  |-  ( th  <->  ps )
64, 5axorbciffatcxorb 27873 . . . 4  |-  ( th
\/_ si )
73, 6pm3.2i 441 . . 3  |-  ( ( ch \/_ ze )  /\  ( th \/_ si ) )
8 mdandyvrx14.5 . . . 4  |-  ( ta  <->  ps )
94, 8axorbciffatcxorb 27873 . . 3  |-  ( ta
\/_ si )
107, 9pm3.2i 441 . 2  |-  ( ( ( ch \/_ ze )  /\  ( th \/_ si ) )  /\  ( ta \/_ si ) )
11 mdandyvrx14.6 . . 3  |-  ( et  <->  ps )
124, 11axorbciffatcxorb 27873 . 2  |-  ( et
\/_ si )
1310, 12pm3.2i 441 1  |-  ( ( ( ( ch \/_ ze )  /\  ( th \/_ si ) )  /\  ( ta \/_ si ) )  /\  ( et \/_ si ) )
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
  Copyright terms: Public domain W3C validator