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Theorem bdnth 15264
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 15263 . 2 BOUNDED
2 fal 1371 . . 3 ¬ ⊥
3 bdnth.1 . . 3 ¬ 𝜑
42, 32false 702 . 2 (⊥ ↔ 𝜑)
51, 4bd0 15254 1 BOUNDED 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wfal 1369  BOUNDED wbd 15242
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 615  ax-in2 616  ax-bd0 15243  ax-bdim 15244  ax-bdn 15247  ax-bdeq 15250
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370
This theorem is referenced by:  bdcnul  15295
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