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Theorem mdandyvr10 27910
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
mdandyvr10.1  |-  ( ph  <->  ze )
mdandyvr10.2  |-  ( ps  <->  si )
mdandyvr10.3  |-  ( ch  <->  ph )
mdandyvr10.4  |-  ( th  <->  ps )
mdandyvr10.5  |-  ( ta  <->  ph )
mdandyvr10.6  |-  ( et  <->  ps )
Assertion
Ref Expression
mdandyvr10  |-  ( ( ( ( ch  <->  ze )  /\  ( th  <->  si )
)  /\  ( ta  <->  ze ) )  /\  ( et 
<-> 
si ) )

Proof of Theorem mdandyvr10
StepHypRef Expression
1 mdandyvr10.2 . 2  |-  ( ps  <->  si )
2 mdandyvr10.1 . 2  |-  ( ph  <->  ze )
3 mdandyvr10.3 . 2  |-  ( ch  <->  ph )
4 mdandyvr10.4 . 2  |-  ( th  <->  ps )
5 mdandyvr10.5 . 2  |-  ( ta  <->  ph )
6 mdandyvr10.6 . 2  |-  ( et  <->  ps )
71, 2, 3, 4, 5, 6mdandyvr5 27905 1  |-  ( ( ( ( ch  <->  ze )  /\  ( th  <->  si )
)  /\  ( ta  <->  ze ) )  /\  ( et 
<-> 
si ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360
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
  Copyright terms: Public domain W3C validator