Theorem bdnth 16197

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 16196	. 2 |- BOUNDED F.
2		fal 1402	. . 3 |- -. F.
3		bdnth.1	. . 3 |- -. ph
4	2, 3	2false 706	. 2 |- ( F. <-> ph )
5	1, 4	bd0 16187	1 |- BOUNDED ph

Syntax hints:   -. wn 3   F. wfal 1400  BOUNDED wbd 16175

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 617  ax-in2 618  ax-bd0 16176  ax-bdim 16177  ax-bdn 16180  ax-bdeq 16183

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-fal 1401

This theorem is referenced by:  bdcnul  16228