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Theorem aiffbbtat 27869
Description: Given a is equivalent to b, b is equivalent to T. there exists a proof for a is equivalent to T. (Contributed by Jarvin Udandy, 29-Aug-2016.)
Hypotheses
Ref Expression
aiffbbtat.1  |-  ( ph  <->  ps )
aiffbbtat.2  |-  ( ps  <->  T.  )
Assertion
Ref Expression
aiffbbtat  |-  ( ph  <->  T.  )

Proof of Theorem aiffbbtat
StepHypRef Expression
1 aiffbbtat.1 . . 3  |-  ( ph  <->  ps )
2 aiffbbtat.2 . . 3  |-  ( ps  <->  T.  )
31, 2pm3.2i 441 . 2  |-  ( (
ph 
<->  ps )  /\  ( ps 
<->  T.  ) )
4 bitr 689 . 2  |-  ( ( ( ph  <->  ps )  /\  ( ps  <->  T.  )
)  ->  ( ph  <->  T.  ) )
53, 4ax-mp 8 1  |-  ( ph  <->  T.  )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    T. wtru 1307
This theorem is referenced by:  dandysum2p2e4  27943  mdandysum2p2e4  27944
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 177  df-an 360
  Copyright terms: Public domain W3C validator