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Theorem tbtru 1546
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 1542 . 2
21tbt 373 1 (𝜑 ↔ (𝜑 ↔ ⊤))
Colors of variables: wff setvar class
Syntax hints:  wb 209  wtru 1539
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 210  df-tru 1541
This theorem is referenced by:  falbitru  1568  tgcgr4  26328  iinabrex  30335  sgn3da  31907  wl-1xor  34892  wl-1mintru1  34898  prjspvs  39591  aistia  43477
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