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Theorem falnantru 1356
Description: A identity. (Contributed by Anthony Hart, 23-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
falnantru (( ⊥ ⊤ ) ↔ ⊤ )

Proof of Theorem falnantru
StepHypRef Expression
1 nancom 1290 . 2 (( ⊥ ⊤ ) ↔ ( ⊤ ⊥ ))
2 trunanfal 1355 . 2 (( ⊤ ⊥ ) ↔ ⊤ )
31, 2bitri 240 1 (( ⊥ ⊤ ) ↔ ⊤ )
Colors of variables: wff setvar class
Syntax hints:  wb 176   wnan 1287  wtru 1316  wfal 1317
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 177  df-an 360  df-nan 1288  df-tru 1319  df-fal 1320
This theorem is referenced by: (None)
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