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Theorem bdnth 9223
Description: A falsity is a bounded formula. (Contributed by BJ, 6-Oct-2019.)
Hypothesis
Ref Expression
bdnth.1 ¬ φ
Assertion
Ref Expression
bdnth BOUNDED φ

Proof of Theorem bdnth
StepHypRef Expression
1 bdfal 9222 . 2 BOUNDED
2 fal 1249 . . 3 ¬ ⊥
3 bdnth.1 . . 3 ¬ φ
42, 32false 616 . 2 ( ⊥ ↔ φ)
51, 4bd0 9213 1 BOUNDED φ
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wfal 1247  BOUNDED wbd 9201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-bd0 9202  ax-bdim 9203  ax-bdn 9206  ax-bdeq 9209
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248
This theorem is referenced by:  bdcnul  9254
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