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Theorem falbitru 1324
Description: A identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
falbitru ((⊥ ↔ ⊤) ↔ ⊥)

Proof of Theorem falbitru
StepHypRef Expression
1 bicom 132 . 2 ((⊥ ↔ ⊤) ↔ (⊤ ↔ ⊥))
2 trubifal 1323 . 2 ((⊤ ↔ ⊥) ↔ ⊥)
31, 2bitri 177 1 ((⊥ ↔ ⊤) ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  wb 102  wtru 1260  wfal 1264
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265
This theorem is referenced by: (None)
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