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Theorem bdnel 9289
Description: Non-membership of a setvar in a bounded formula is a bounded formula. (Contributed by BJ, 16-Oct-2019.)
Hypothesis
Ref Expression
bdnel.1 BOUNDED A
Assertion
Ref Expression
bdnel BOUNDED xA
Distinct variable group:   x,A

Proof of Theorem bdnel
StepHypRef Expression
1 bdnel.1 . . . 4 BOUNDED A
21bdeli 9281 . . 3 BOUNDED x A
32ax-bdn 9252 . 2 BOUNDED ¬ x A
4 df-nel 2204 . 2 (xA ↔ ¬ x A)
53, 4bd0r 9260 1 BOUNDED xA
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   wcel 1390  wnel 2202  BOUNDED wbd 9247  BOUNDED wbdc 9275
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-4 1397  ax-bd0 9248  ax-bdn 9252
This theorem depends on definitions:  df-bi 110  df-nel 2204  df-bdc 9276
This theorem is referenced by: (None)
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