Theorem bdfal 9953

Description: The truth value ⊥ is bounded. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdfal	⊢ BOUNDED ⊥

Proof of Theorem bdfal

Step	Hyp	Ref	Expression
1		bdtru 9952	. . 3 ⊢ BOUNDED ⊤
2	1	ax-bdn 9937	. 2 ⊢ BOUNDED ¬ ⊤
3		df-fal 1249	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	bd0r 9945	1 ⊢ BOUNDED ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1244  ⊥wfal 1248  BOUNDED wbd 9932

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-bd0 9933  ax-bdim 9934  ax-bdn 9937  ax-bdeq 9940

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249

This theorem is referenced by:  bdnth  9954  bj-axemptylem  10012