Users' Mathboxes Mathbox for Jarvin Udandy < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  aistia Structured version   Unicode version

Theorem aistia 37473
Description: Given a is equivalent to T., there exists a proof for a. (Contributed by Jarvin Udandy, 30-Aug-2016.)
Hypothesis
Ref Expression
aistia.1  |-  ( ph  <-> T.  )
Assertion
Ref Expression
aistia  |-  ph

Proof of Theorem aistia
StepHypRef Expression
1 aistia.1 . 2  |-  ( ph  <-> T.  )
2 tbtru 1417 . 2  |-  ( ph  <->  (
ph 
<-> T.  ) )
31, 2mpbir 211 1  |-  ph
Colors of variables: wff setvar class
Syntax hints:    <-> wb 186   T. wtru 1408
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 187  df-tru 1410
This theorem is referenced by:  astbstanbst  37485  aistbistaandb  37486  aistbisfiaxb  37496  aisfbistiaxb  37497  dandysum2p2e4  37551
  Copyright terms: Public domain W3C validator