Theorem bdnth 13716

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 13715	. 2 |- BOUNDED F.
2		fal 1350	. . 3 |- -. F.
3		bdnth.1	. . 3 |- -. ph
4	2, 3	2false 691	. 2 |- ( F. <-> ph )
5	1, 4	bd0 13706	1 |- BOUNDED ph

Syntax hints:   -. wn 3   F. wfal 1348  BOUNDED wbd 13694

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-in1 604  ax-in2 605  ax-bd0 13695  ax-bdim 13696  ax-bdn 13699  ax-bdeq 13702

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-fal 1349

This theorem is referenced by:  bdcnul  13747