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Theorem bdelir 13129
Description: Inference associated with df-bdc 13123. Its converse is bdeli 13128. (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 13123 . 2  |-  (BOUNDED  A  <->  A. xBOUNDED  x  e.  A )
2 bdelir.1 . 2  |- BOUNDED  x  e.  A
31, 2mpgbir 1429 1  |- BOUNDED  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1480  BOUNDED wbd 13094  BOUNDED wbdc 13122
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1425
This theorem depends on definitions:  df-bi 116  df-bdc 13123
This theorem is referenced by:  bdcv  13130  bdcab  13131  bdcvv  13139  bdcnul  13147  bdop  13157
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