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Theorem bdnth 12834
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 12833 . 2 BOUNDED
2 fal 1321 . . 3 ¬ ⊥
3 bdnth.1 . . 3 ¬ 𝜑
42, 32false 673 . 2 (⊥ ↔ 𝜑)
51, 4bd0 12824 1 BOUNDED 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wfal 1319  BOUNDED wbd 12812
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 586  ax-in2 587  ax-bd0 12813  ax-bdim 12814  ax-bdn 12817  ax-bdeq 12820
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320
This theorem is referenced by:  bdcnul  12865
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