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

Theorem tbtru 1548
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 1544 . 2
21tbt 369 1 (𝜑 ↔ (𝜑 ↔ ⊤))
Colors of variables: wff setvar class
Syntax hints:  wb 206  wtru 1541
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 207  df-tru 1543
This theorem is referenced by:  falbitru  1570  ab0orv  4383  tgcgr4  28539  iinabrex  32582  sgn3da  34544  wl-1xor  37483  wl-1mintru1  37489  prjspvs  42620  aistia  46909
  Copyright terms: Public domain W3C validator