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Theorem mdandyvr15 27587
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
mdandyvr15.1  |-  ( ph  <->  ze )
mdandyvr15.2  |-  ( ps  <->  si )
mdandyvr15.3  |-  ( ch  <->  ps )
mdandyvr15.4  |-  ( th  <->  ps )
mdandyvr15.5  |-  ( ta  <->  ps )
mdandyvr15.6  |-  ( et  <->  ps )
Assertion
Ref Expression
mdandyvr15  |-  ( ( ( ( ch  <->  si )  /\  ( th  <->  si )
)  /\  ( ta  <->  si ) )  /\  ( et 
<-> 
si ) )

Proof of Theorem mdandyvr15
StepHypRef Expression
1 mdandyvr15.2 . 2  |-  ( ps  <->  si )
2 mdandyvr15.1 . 2  |-  ( ph  <->  ze )
3 mdandyvr15.3 . 2  |-  ( ch  <->  ps )
4 mdandyvr15.4 . 2  |-  ( th  <->  ps )
5 mdandyvr15.5 . 2  |-  ( ta  <->  ps )
6 mdandyvr15.6 . 2  |-  ( et  <->  ps )
71, 2, 3, 4, 5, 6mdandyvr0 27572 1  |-  ( ( ( ( ch  <->  si )  /\  ( th  <->  si )
)  /\  ( 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
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