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Theorem bdeli 13058
Description: Inference associated with bdel 13057. Its converse is bdelir 13059. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdeli.1  |- BOUNDED  A
Assertion
Ref Expression
bdeli  |- BOUNDED  x  e.  A
Distinct variable group:    x, A

Proof of Theorem bdeli
StepHypRef Expression
1 bdeli.1 . 2  |- BOUNDED  A
2 bdel 13057 . 2  |-  (BOUNDED  A  -> BOUNDED  x  e.  A )
31, 2ax-mp 5 1  |- BOUNDED  x  e.  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1480  BOUNDED wbd 13024  BOUNDED wbdc 13052
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1487
This theorem depends on definitions:  df-bi 116  df-bdc 13053
This theorem is referenced by:  bdph  13062  bdcrab  13064  bdnel  13066  bdccsb  13072  bdcdif  13073  bdcun  13074  bdcin  13075  bdss  13076  bdsnss  13085  bdciun  13090  bdciin  13091  bdinex1  13111  bj-uniex2  13128  bj-inf2vnlem3  13184
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