Users' Mathboxes Mathbox for Jarvin Udandy < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  mdandyvrx10 Structured version   Unicode version

Theorem mdandyvrx10 27950
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
mdandyvrx10.1  |-  ( ph  \/_ 
ze )
mdandyvrx10.2  |-  ( ps 
\/_  si )
mdandyvrx10.3  |-  ( ch  <->  ph )
mdandyvrx10.4  |-  ( th  <->  ps )
mdandyvrx10.5  |-  ( ta  <->  ph )
mdandyvrx10.6  |-  ( et  <->  ps )
Assertion
Ref Expression
mdandyvrx10  |-  ( ( ( ( ch  \/_  ze )  /\  ( th 
\/_  si ) )  /\  ( ta  \/_  ze )
)  /\  ( et  \/_  si ) )

Proof of Theorem mdandyvrx10
StepHypRef Expression
1 mdandyvrx10.2 . 2  |-  ( ps 
\/_  si )
2 mdandyvrx10.1 . 2  |-  ( ph  \/_ 
ze )
3 mdandyvrx10.3 . 2  |-  ( ch  <->  ph )
4 mdandyvrx10.4 . 2  |-  ( th  <->  ps )
5 mdandyvrx10.5 . 2  |-  ( ta  <->  ph )
6 mdandyvrx10.6 . 2  |-  ( et  <->  ps )
71, 2, 3, 4, 5, 6mdandyvrx5 27945 1  |-  ( ( ( ( ch  \/_  ze )  /\  ( th 
\/_  si ) )  /\  ( ta  \/_  ze )
)  /\  ( et  \/_  si ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360    \/_ wxo 1314
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 179  df-an 362  df-xor 1315
  Copyright terms: Public domain W3C validator