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Theorem mdandyvrx12 27916
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  |-  ( ph  \/_ 
ze )
mdandyvrx12.2  |-  ( ps 
\/_  si )
mdandyvrx12.3  |-  ( ch  <->  ph )
mdandyvrx12.4  |-  ( th  <->  ph )
mdandyvrx12.5  |-  ( ta  <->  ps )
mdandyvrx12.6  |-  ( et  <->  ps )
Assertion
Ref Expression
mdandyvrx12  |-  ( ( ( ( ch  \/_  ze )  /\  ( th 
\/_  ze ) )  /\  ( ta  \/_  si )
)  /\  ( et  \/_  si ) )

Proof of Theorem mdandyvrx12
StepHypRef Expression
1 mdandyvrx12.2 . 2  |-  ( ps 
\/_  si )
2 mdandyvrx12.1 . 2  |-  ( ph  \/_ 
ze )
3 mdandyvrx12.3 . 2  |-  ( ch  <->  ph )
4 mdandyvrx12.4 . 2  |-  ( th  <->  ph )
5 mdandyvrx12.5 . 2  |-  ( ta  <->  ps )
6 mdandyvrx12.6 . 2  |-  ( et  <->  ps )
71, 2, 3, 4, 5, 6mdandyvrx3 27907 1  |-  ( ( ( ( ch  \/_  ze )  /\  ( th 
\/_  ze ) )  /\  ( ta  \/_  si )
)  /\  ( et  \/_  si ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360    \/_ wxo 1314
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 179  df-an 362  df-xor 1315
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