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Theorem bdeli 12971
Description: Inference associated with bdel 12970. Its converse is bdelir 12972. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdeli.1 BOUNDED 𝐴
Assertion
Ref Expression
bdeli BOUNDED 𝑥𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem bdeli
StepHypRef Expression
1 bdeli.1 . 2 BOUNDED 𝐴
2 bdel 12970 . 2 (BOUNDED 𝐴BOUNDED 𝑥𝐴)
31, 2ax-mp 5 1 BOUNDED 𝑥𝐴
Colors of variables: wff set class
Syntax hints:  wcel 1465  BOUNDED wbd 12937  BOUNDED wbdc 12965
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1472
This theorem depends on definitions:  df-bi 116  df-bdc 12966
This theorem is referenced by:  bdph  12975  bdcrab  12977  bdnel  12979  bdccsb  12985  bdcdif  12986  bdcun  12987  bdcin  12988  bdss  12989  bdsnss  12998  bdciun  13003  bdciin  13004  bdinex1  13024  bj-uniex2  13041  bj-inf2vnlem3  13097
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