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Theorem bdelir 9282
Description: Inference associated with df-bdc 9276. Its converse is bdeli 9281. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdelir.1 BOUNDED x A
Assertion
Ref Expression
bdelir BOUNDED A
Distinct variable group:   x,A

Proof of Theorem bdelir
StepHypRef Expression
1 df-bdc 9276 . 2 (BOUNDED AxBOUNDED x A)
2 bdelir.1 . 2 BOUNDED x A
31, 2mpgbir 1339 1 BOUNDED A
Colors of variables: wff set class
Syntax hints:   wcel 1390  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-gen 1335
This theorem depends on definitions:  df-bi 110  df-bdc 9276
This theorem is referenced by:  bdcv  9283  bdcab  9284  bdcvv  9292  bdcnul  9300  bdop  9310
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