Theorem bdfal 15587

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 15586	. . 3 |- BOUNDED T.
2	1	ax-bdn 15571	. 2 |- BOUNDED -. T.
3		df-fal 1370	. 2 |- ( F. <-> -. T. )
4	2, 3	bd0r 15579	1 |- BOUNDED F.

Syntax hints:   -. wn 3   T. wtru 1365   F. wfal 1369  BOUNDED wbd 15566

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 15567  ax-bdim 15568  ax-bdn 15571  ax-bdeq 15574

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370

This theorem is referenced by:  bdnth  15588  bj-axemptylem  15646