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

Theorem falbitru 1683
Description: A identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 10-Jul-2020.)
Assertion
Ref Expression
falbitru ((⊥ ↔ ⊤) ↔ ⊥)

Proof of Theorem falbitru
StepHypRef Expression
1 tbtru 1661 . 2 (⊥ ↔ (⊥ ↔ ⊤))
21bicomi 215 1 ((⊥ ↔ ⊤) ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  wb 197  wtru 1653  wfal 1665
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 198  df-tru 1656
This theorem is referenced by:  trubifal  1684
  Copyright terms: Public domain W3C validator