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Theorem bdeli 7073
Description: Inference associated with bdel 7072. Its converse is bdelir 7074. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdeli.1 BOUNDED A
Assertion
Ref Expression
bdeli BOUNDED x A
Distinct variable group:   x,A

Proof of Theorem bdeli
StepHypRef Expression
1 bdeli.1 . 2 BOUNDED A
2 bdel 7072 . 2 (BOUNDED ABOUNDED x A)
31, 2ax-mp 7 1 BOUNDED x A
Colors of variables: wff set class
Syntax hints:   wcel 1374  BOUNDED wbd 7039  BOUNDED wbdc 7067
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-4 1381
This theorem depends on definitions:  df-bi 110  df-bdc 7068
This theorem is referenced by:  bdph  7077  bdcrab  7079  bdnel  7081  bdccsb  7087  bdcdif  7088  bdcun  7089  bdcin  7090  bdss  7091  bdsnss  7100  bdciun  7105  bdciin  7106  bdinex1  7122  bj-uniex2  7139  bj-inf2vnlem3  7190
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