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Theorem bdceqi 9963
Description: A class equal to a bounded one is bounded. Note the use of ax-ext 2022. See also bdceqir 9964. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bdceqi.min  |- BOUNDED  A
bdceqi.maj  |-  A  =  B
Assertion
Ref Expression
bdceqi  |- BOUNDED  B

Proof of Theorem bdceqi
StepHypRef Expression
1 bdceqi.min . 2  |- BOUNDED  A
2 bdceqi.maj . . 3  |-  A  =  B
32bdceq 9962 . 2  |-  (BOUNDED  A  <-> BOUNDED  B )
41, 3mpbi 133 1  |- BOUNDED  B
Colors of variables: wff set class
Syntax hints:    = wceq 1243  BOUNDED wbdc 9960
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-bd0 9933
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-clel 2036  df-bdc 9961
This theorem is referenced by:  bdceqir  9964  bds  9971  bdcuni  9996
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