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Theorem bdfal 11381
Description: The truth value is bounded. (Contributed by BJ, 3-Oct-2019.)
Assertion
Ref Expression
bdfal BOUNDED

Proof of Theorem bdfal
StepHypRef Expression
1 bdtru 11380 . . 3 BOUNDED
21ax-bdn 11365 . 2 BOUNDED ¬ ⊤
3 df-fal 1295 . 2 (⊥ ↔ ¬ ⊤)
42, 3bd0r 11373 1 BOUNDED
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wtru 1290  wfal 1294  BOUNDED wbd 11360
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-bd0 11361  ax-bdim 11362  ax-bdn 11365  ax-bdeq 11368
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295
This theorem is referenced by:  bdnth  11382  bj-axemptylem  11440
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