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Theorem bdeli 9966
 Description: Inference associated with bdel 9965. Its converse is bdelir 9967. (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 9965 . 2 (BOUNDED 𝐴BOUNDED 𝑥𝐴)
31, 2ax-mp 7 1 BOUNDED 𝑥𝐴
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1393  BOUNDED wbd 9932  BOUNDED wbdc 9960 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-4 1400 This theorem depends on definitions:  df-bi 110  df-bdc 9961 This theorem is referenced by:  bdph  9970  bdcrab  9972  bdnel  9974  bdccsb  9980  bdcdif  9981  bdcun  9982  bdcin  9983  bdss  9984  bdsnss  9993  bdciun  9998  bdciin  9999  bdinex1  10019  bj-uniex2  10036  bj-inf2vnlem3  10097
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