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Theorem bdelir 15036
Description: Inference associated with df-bdc 15030. Its converse is bdeli 15035. (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 15030 . 2 (BOUNDED 𝐴 ↔ ∀𝑥BOUNDED 𝑥𝐴)
2 bdelir.1 . 2 BOUNDED 𝑥𝐴
31, 2mpgbir 1464 1 BOUNDED 𝐴
Colors of variables: wff set class
Syntax hints:  wcel 2160  BOUNDED wbd 15001  BOUNDED wbdc 15029
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-gen 1460
This theorem depends on definitions:  df-bi 117  df-bdc 15030
This theorem is referenced by:  bdcv  15037  bdcab  15038  bdcvv  15046  bdcnul  15054  bdop  15064
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