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Theorem bdfal 10891
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 10890 . . 3 BOUNDED
21ax-bdn 10875 . 2 BOUNDED ¬ ⊤
3 df-fal 1291 . 2 (⊥ ↔ ¬ ⊤)
42, 3bd0r 10883 1 BOUNDED
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wtru 1286  wfal 1290  BOUNDED wbd 10870
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 10871  ax-bdim 10872  ax-bdn 10875  ax-bdeq 10878
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291
This theorem is referenced by:  bdnth  10892  bj-axemptylem  10950
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