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Theorem falbitru 1305
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 128 . 2 (( ⊥ ↔ ⊤ ) ↔ ( ⊤ ↔ ⊥ ))
2 trubifal 1304 . 2 (( ⊤ ↔ ⊥ ) ↔ ⊥ )
31, 2bitri 173 1 (( ⊥ ↔ ⊤ ) ↔ ⊥ )
Colors of variables: wff set class
Syntax hints:  wb 98  wtru 1243  wfal 1247
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248
This theorem is referenced by: (None)
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