Theorem bdfal 13020

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 13019	. . 3 ⊢ BOUNDED ⊤
2	1	ax-bdn 13004	. 2 ⊢ BOUNDED ¬ ⊤
3		df-fal 1337	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	bd0r 13012	1 ⊢ BOUNDED ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1332  ⊥wfal 1336  BOUNDED wbd 12999

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 13000  ax-bdim 13001  ax-bdn 13004  ax-bdeq 13007

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337

This theorem is referenced by:  bdnth  13021  bj-axemptylem  13079