Theorem bdfal 11381

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 11380	. . 3 |- BOUNDED T.
2	1	ax-bdn 11365	. 2 |- BOUNDED -. T.
3		df-fal 1295	. 2 |- ( F. <-> -. T. )
4	2, 3	bd0r 11373	1 |- BOUNDED F.

Syntax hints:   -. wn 3   T. wtru 1290   F. wfal 1294  BOUNDED wbd 11360

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 11361  ax-bdim 11362  ax-bdn 11365  ax-bdeq 11368

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295

This theorem is referenced by:  bdnth  11382  bj-axemptylem  11440