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Theorem bdelir 11095
Description: Inference associated with df-bdc 11089. Its converse is bdeli 11094. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdelir.1  |- BOUNDED  x  e.  A
Assertion
Ref Expression
bdelir  |- BOUNDED  A
Distinct variable group:    x, A

Proof of Theorem bdelir
StepHypRef Expression
1 df-bdc 11089 . 2  |-  (BOUNDED  A  <->  A. xBOUNDED  x  e.  A )
2 bdelir.1 . 2  |- BOUNDED  x  e.  A
31, 2mpgbir 1385 1  |- BOUNDED  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1436  BOUNDED wbd 11060  BOUNDED wbdc 11088
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1381
This theorem depends on definitions:  df-bi 115  df-bdc 11089
This theorem is referenced by:  bdcv  11096  bdcab  11097  bdcvv  11105  bdcnul  11113  bdop  11123
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