MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  tbtru Unicode version

Theorem tbtru 1315
Description: If something is true, it outputs  T.. (Contributed by Anthony Hart, 14-Aug-2011.)
Assertion
Ref Expression
tbtru  |-  ( ph  <->  (
ph 
<->  T.  ) )

Proof of Theorem tbtru
StepHypRef Expression
1 tru 1312 . 2  |-  T.
21tbt 333 1  |-  ( ph  <->  (
ph 
<->  T.  ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    T. wtru 1307
This theorem is referenced by:  aistia  27865
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-tru 1310
  Copyright terms: Public domain W3C validator