Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bdfal GIF version

Theorem bdfal 15270
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 15269 . . 3 BOUNDED
21ax-bdn 15254 . 2 BOUNDED ¬ ⊤
3 df-fal 1370 . 2 (⊥ ↔ ¬ ⊤)
42, 3bd0r 15262 1 BOUNDED
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wtru 1365  wfal 1369  BOUNDED wbd 15249
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-bd0 15250  ax-bdim 15251  ax-bdn 15254  ax-bdeq 15257
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370
This theorem is referenced by:  bdnth  15271  bj-axemptylem  15329
  Copyright terms: Public domain W3C validator