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Theorem mdandyvr12 27898
Description: Given the equivalences set in the hypotheses, there exist a proof where ch, th, ta, et match ze, si accordingly (Contributed by Jarvin Udandy, 7-Sep-2016.)
Hypotheses
Ref Expression
mdandyvr12.1  |-  ( ph  <->  ze )
mdandyvr12.2  |-  ( ps  <->  si )
mdandyvr12.3  |-  ( ch  <->  ph )
mdandyvr12.4  |-  ( th  <->  ph )
mdandyvr12.5  |-  ( ta  <->  ps )
mdandyvr12.6  |-  ( et  <->  ps )
Assertion
Ref Expression
mdandyvr12  |-  ( ( ( ( ch  <->  ze )  /\  ( th  <->  ze )
)  /\  ( ta  <->  si ) )  /\  ( et 
<-> 
si ) )

Proof of Theorem mdandyvr12
StepHypRef Expression
1 mdandyvr12.2 . 2  |-  ( ps  <->  si )
2 mdandyvr12.1 . 2  |-  ( ph  <->  ze )
3 mdandyvr12.3 . 2  |-  ( ch  <->  ph )
4 mdandyvr12.4 . 2  |-  ( th  <->  ph )
5 mdandyvr12.5 . 2  |-  ( ta  <->  ps )
6 mdandyvr12.6 . 2  |-  ( et  <->  ps )
71, 2, 3, 4, 5, 6mdandyvr3 27889 1  |-  ( ( ( ( ch  <->  ze )  /\  ( th  <->  ze )
)  /\  ( ta  <->  si ) )  /\  ( et 
<-> 
si ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359
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
  Copyright terms: Public domain W3C validator