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Theorem bdeli 15056
Description: Inference associated with bdel 15055. Its converse is bdelir 15057. (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 15055 . 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 2160  BOUNDED wbd 15022  BOUNDED wbdc 15050
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1521
This theorem depends on definitions:  df-bi 117  df-bdc 15051
This theorem is referenced by:  bdph  15060  bdcrab  15062  bdnel  15064  bdccsb  15070  bdcdif  15071  bdcun  15072  bdcin  15073  bdss  15074  bdsnss  15083  bdciun  15088  bdciin  15089  bdinex1  15109  bj-uniex2  15126  bj-inf2vnlem3  15182
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