Theorem bdnth 10625

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 10624	. 2 |- BOUNDED F.
2		fal 1291	. . 3 |- -. F.
3		bdnth.1	. . 3 |- -. ph
4	2, 3	2false 649	. 2 |- ( F. <-> ph )
5	1, 4	bd0 10615	1 |- BOUNDED ph

Syntax hints:   -. wn 3   F. wfal 1289  BOUNDED wbd 10603

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-in1 576  ax-in2 577  ax-bd0 10604  ax-bdim 10605  ax-bdn 10608  ax-bdeq 10611

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by:  bdcnul  10656