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Theorem aiffbtbat 27852
Description: Given a is equivalent to b, T. is equivalent to b. there exists a proof for a is equivalent to T. (Contributed by Jarvin Udandy, 29-Aug-2016.)
Hypotheses
Ref Expression
aiffbtbat.1  |-  ( ph  <->  ps )
aiffbtbat.2  |-  (  T.  <->  ps )
Assertion
Ref Expression
aiffbtbat  |-  ( ph  <->  T.  )

Proof of Theorem aiffbtbat
StepHypRef Expression
1 aiffbtbat.1 . 2  |-  ( ph  <->  ps )
2 aiffbtbat.2 . 2  |-  (  T.  <->  ps )
31, 2bitr4i 244 1  |-  ( ph  <->  T.  )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    T. wtru 1325
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
  Copyright terms: Public domain W3C validator