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

Theorem bdfal 12833
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 12832 . . 3 BOUNDED
21ax-bdn 12817 . 2 BOUNDED ¬ ⊤
3 df-fal 1320 . 2 (⊥ ↔ ¬ ⊤)
42, 3bd0r 12825 1 BOUNDED
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wtru 1315  wfal 1319  BOUNDED wbd 12812
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-bd0 12813  ax-bdim 12814  ax-bdn 12817  ax-bdeq 12820
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320
This theorem is referenced by:  bdnth  12834  bj-axemptylem  12892
  Copyright terms: Public domain W3C validator