Theorem bdfal 14670

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 14669	. . 3 ⊢ BOUNDED ⊤
2	1	ax-bdn 14654	. 2 ⊢ BOUNDED ¬ ⊤
3		df-fal 1359	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	bd0r 14662	1 ⊢ BOUNDED ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1354  ⊥wfal 1358  BOUNDED wbd 14649

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 14650  ax-bdim 14651  ax-bdn 14654  ax-bdeq 14657

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-fal 1359

This theorem is referenced by:  bdnth  14671  bj-axemptylem  14729