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Theorem bdnth 14208
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 14207 . 2  |- BOUNDED F.
2 fal 1360 . . 3  |-  -. F.
3 bdnth.1 . . 3  |-  -.  ph
42, 32false 701 . 2  |-  ( F.  <->  ph )
51, 4bd0 14198 1  |- BOUNDED  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3   F. wfal 1358  BOUNDED wbd 14186
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 614  ax-in2 615  ax-bd0 14187  ax-bdim 14188  ax-bdn 14191  ax-bdeq 14194
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-fal 1359
This theorem is referenced by:  bdcnul  14239
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