Theorem bdnth 15064

Description: A falsity is a bounded formula. (Contributed by BJ, 6-Oct-2019.)

Hypothesis

Ref	Expression
bdnth.1	|- -. ph

Assertion

Ref	Expression
bdnth	|- BOUNDED ph

Proof of Theorem bdnth

Step	Hyp	Ref	Expression
1		bdfal 15063	. 2 |- BOUNDED F.
2		fal 1371	. . 3 |- -. F.
3		bdnth.1	. . 3 |- -. ph
4	2, 3	2false 702	. 2 |- ( F. <-> ph )
5	1, 4	bd0 15054	1 |- BOUNDED ph

Syntax hints:   -. wn 3   F. wfal 1369  BOUNDED wbd 15042

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-in1 615  ax-in2 616  ax-bd0 15043  ax-bdim 15044  ax-bdn 15047  ax-bdeq 15050

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

This theorem is referenced by:  bdcnul  15095