Theorem bdfal 13020

Description: The truth value F. is bounded. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdfal	|- BOUNDED F.

Proof of Theorem bdfal

Step	Hyp	Ref	Expression
1		bdtru 13019	. . 3 |- BOUNDED T.
2	1	ax-bdn 13004	. 2 |- BOUNDED -. T.
3		df-fal 1337	. 2 |- ( F. <-> -. T. )
4	2, 3	bd0r 13012	1 |- BOUNDED F.

Syntax hints:   -. wn 3   T. wtru 1332   F. 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