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Theorem bdeli 14534
Description: Inference associated with bdel 14533. Its converse is bdelir 14535. (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 14533 . 2 (BOUNDED 𝐴BOUNDED 𝑥𝐴)
31, 2ax-mp 5 1 BOUNDED 𝑥𝐴
Colors of variables: wff set class
Syntax hints:  wcel 2148  BOUNDED wbd 14500  BOUNDED wbdc 14528
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1510
This theorem depends on definitions:  df-bi 117  df-bdc 14529
This theorem is referenced by:  bdph  14538  bdcrab  14540  bdnel  14542  bdccsb  14548  bdcdif  14549  bdcun  14550  bdcin  14551  bdss  14552  bdsnss  14561  bdciun  14566  bdciin  14567  bdinex1  14587  bj-uniex2  14604  bj-inf2vnlem3  14660
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