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Theorem bdnth 10783
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 10782 . 2  |- BOUNDED F.
2 fal 1292 . . 3  |-  -. F.
3 bdnth.1 . . 3  |-  -.  ph
42, 32false 650 . 2  |-  ( F.  <->  ph )
51, 4bd0 10773 1  |- BOUNDED  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3   F. wfal 1290  BOUNDED wbd 10761
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 577  ax-in2 578  ax-bd0 10762  ax-bdim 10763  ax-bdn 10766  ax-bdeq 10769
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291
This theorem is referenced by:  bdcnul  10814
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