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Theorem bdnth 13085
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
StepHypRef Expression
1 bdfal 13084 . 2  |- BOUNDED F.
2 fal 1338 . . 3  |-  -. F.
3 bdnth.1 . . 3  |-  -.  ph
42, 32false 690 . 2  |-  ( F.  <->  ph )
51, 4bd0 13075 1  |- BOUNDED  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3   F. wfal 1336  BOUNDED wbd 13063
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 603  ax-in2 604  ax-bd0 13064  ax-bdim 13065  ax-bdn 13068  ax-bdeq 13071
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337
This theorem is referenced by:  bdcnul  13116
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