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

Theorem tbtru 1534
Description: A proposition is equivalent to itself being equivalent to . (Contributed by Anthony Hart, 14-Aug-2011.)
Assertion
Ref Expression
tbtru (𝜑 ↔ (𝜑 ↔ ⊤))

Proof of Theorem tbtru
StepHypRef Expression
1 tru 1527 . 2
21tbt 358 1 (𝜑 ↔ (𝜑 ↔ ⊤))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wtru 1524
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 197  df-tru 1526
This theorem is referenced by:  falbitru  1561  tgcgr4  25471  sgn3da  30731  aistia  41385
  Copyright terms: Public domain W3C validator