Theorem bdfal 16428

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 16427	. . 3 ⊢ BOUNDED ⊤
2	1	ax-bdn 16412	. 2 ⊢ BOUNDED ¬ ⊤
3		df-fal 1403	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	bd0r 16420	1 ⊢ BOUNDED ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1398  ⊥wfal 1402  BOUNDED wbd 16407

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 16408  ax-bdim 16409  ax-bdn 16412  ax-bdeq 16415

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-fal 1403

This theorem is referenced by:  bdnth  16429  bj-axemptylem  16487