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Theorem tbtru 1542
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 1538 . 2
21tbt 368 1 (𝜑 ↔ (𝜑 ↔ ⊤))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wtru 1535
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 206  df-tru 1537
This theorem is referenced by:  falbitru  1564  ab0orv  4383  tgcgr4  28458  iinabrex  32489  sgn3da  34375  wl-1xor  37189  wl-1mintru1  37195  prjspvs  42264  aistia  46512
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