Theorem bdfal 10624

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 10623	. . 3 ⊢ BOUNDED ⊤
2	1	ax-bdn 10608	. 2 ⊢ BOUNDED ¬ ⊤
3		df-fal 1290	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	bd0r 10616	1 ⊢ BOUNDED ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1285  ⊥wfal 1289  BOUNDED wbd 10603

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-bd0 10604  ax-bdim 10605  ax-bdn 10608  ax-bdeq 10611

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by:  bdnth  10625  bj-axemptylem  10683