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Theorem bdelir 10889
Description: Inference associated with df-bdc 10883. Its converse is bdeli 10888. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdelir.1 BOUNDED 𝑥𝐴
Assertion
Ref Expression
bdelir BOUNDED 𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem bdelir
StepHypRef Expression
1 df-bdc 10883 . 2 (BOUNDED 𝐴 ↔ ∀𝑥BOUNDED 𝑥𝐴)
2 bdelir.1 . 2 BOUNDED 𝑥𝐴
31, 2mpgbir 1383 1 BOUNDED 𝐴
Colors of variables: wff set class
Syntax hints:  wcel 1434  BOUNDED wbd 10854  BOUNDED wbdc 10882
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1379
This theorem depends on definitions:  df-bi 115  df-bdc 10883
This theorem is referenced by:  bdcv  10890  bdcab  10891  bdcvv  10899  bdcnul  10907  bdop  10917
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