Theorem bdfal 17025

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 17024	. . 3 ⊢ BOUNDED ⊤
2	1	ax-bdn 17009	. 2 ⊢ BOUNDED ¬ ⊤
3		df-fal 1408	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	bd0r 17017	1 ⊢ BOUNDED ⊥

This proof depends on syntax axioms:  ¬ wn 3  ⊤wtru 1403  ⊥wfal 1407  BOUNDED wbd 17004

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-bd0 17005  ax-bdim 17006  ax-bdn 17009  ax-bdeq 17012

This proof depends on definitions:  df-bi 117  df-tru 1405  df-fal 1408

This theorem is used by:  bdnth  17026  bj-axemptylem  17084